Bibliography of Elliptic Hypergeometric Functions

The address of this page is
http://www.math.chalmers.se/~hjalmar/bibliography.html

Compiled by Hjalmar Rosengren. Last updated 15 August 2023.
Elliptic hypergeometric functions first appeared in Date et al. (1988), and more explicitly in Frenkel and Turaev (1997). For an introduction, see Van de Bult (2017), Chapter 11 of Gasper & Rahman (2004), Rosengren (2016) or Spiridonov (2008). When compiling this bibliography, I have restricted myself to publications where elliptic hypergeometric sums or integrals appear explicitly, deliberately excluding many relevant papers on closely related topics.

Please send corrections, additions and comments to hjalmarATchalmersDOTse

I would like to thank Seamus Albion, Fokko van de Bult, Ilmar Gahramanov, Eric Rains, Michael Schlosser, Slava Spiridonov, Jasper Stokman, Alexander Varchenko, Alexei Zhedanov and Wadim Zudilin for useful comments.
  1. A. Aggarwal, Dynamical stochastic higher spin vertex models, Selecta Math. 24 (2018), 2659-2735, 1704.02499.
  2. A. Aggarwal, A. Borodin and A. Bufetov, Stochasticization of solutions to the Yang-Baxter equation, Ann. Henri Poincaré 20 (2019), 2495–2554, 1810.04299.
  3. P. Aggarwal, K. Maruyoshi and J. Song, A "Lagrangian" for the E7 superconformal theory, 1802.05268.
  4. O. Aharony, S. S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, J. High Energy Phys. 2013, 149, 1305.3924.
  5. S. P. Albion, E. M. Rains and S. O. Warnaar, AFLT-type Selberg integrals, 2001.05637.
  6. S. P. Albion, E. M. Rains and S. O. Warnaar, Elliptic An Selberg integrals, 2306.02442 .
  7. A. Amariti, Integral identities for 3d dualities with SP(2N) gauge groups, 1509.02199.
  8. A. Amariti and C. Klare, A journey to 3d: exact relations for adjoint SQCD from dimensional reduction. J. High Energy Phys. 2015, 148, 1409.8623.
  9. E. Apresyan, G. Sarkissian and V. P. Spiridonov, A parafermionic hypergeometric function and supersymmetric 6j-symbols, 2205.10276.
  10. A. A. Ardehali, High-temperature asymptotics of supersymmetric partition functions, J. High Energy Phys. 2016, 025, 1512.03376.
  11. A. A. Ardehali, High-temperature Asymptotics of the 4d Superconformal Index, PhD thesis, University of Michigan, 2016, 1605.06100..
  12. A. A. Ardehali, The hyperbolic asymptotics of elliptic hypergeometric integrals arising in supersymmetric gauge theory, SIGMA 14 (2018), 043, 1712.09933.
  13. A. A. Ardehali, Cardy-like asymptotics of the 4d N=4 index and AdS5 black holes, J. High Energy Phys. 2019, 134, 1902.06619.
  14. C. E. Arreche, T. Dreyfus and J. Roques, On the differential transcendence of the elliptic hypergeometric functions, 1809.05416.
  15. F. Atai and M. Noumi, Eigenfunctions of the van Diejen model generated by gauge and integral transformations, 2203.00498.
  16. H. Baba and M. Katori, Excursion processes associated with elliptic combinatorics, J. Stat. Phys. 171 (2018), 1035-1066, 1711.00389.
  17. I. Bah, A. Hanany, K. Maruyoshi, S. S. Razamat, Y. Tachikawa and G. Zafrir, 4d N=1 from 6d N=(1,0) on a torus with fluxes, J. High Energy Phys. 2017, 022, 1702.04740..
  18. V. V. Bazhanov, A. P. Kels and S. M. Sergeev, Comment on star-star relations in statistical mechanics and elliptic gamma function identities, J. Phys. A 46 (2013), 152001, 1301.5775.
  19. V. V. Bazhanov and S. M. Sergeev, A master solution of the quantum Yang-Baxter equation and classical discrete integrable equations, Adv. Theor. Math. Phys. 16 (2012), 65-95, 1006.0651.
  20. V. V. Bazhanov and S. M. Sergeev, Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation, Nuclear Phys. B 856 (2012), 475-496, 1106.5874.
  21. C. Beem and A. Gadde, The superconformal index of N=1 class S fixed points , J. High Energy Phys. 2014, 36, 1212.1467.
  22. N. Belousov, S. Derkachov, S. Kharchev and S. Khoroshkin, Hypergeometric identities related to Ruijsenaars system, 2303.07350.
  23. F. Benini and P. Milan, A Bethe Ansatz type formula for the superconformal index, 1811.04107.
  24. D. Betea, Elliptic Combinatorics and Markov Processes, PhD thesis, California Institute of Technology, 2012.
  25. D. Betea, Elliptically distributed lozenge tilings of a hexagon, SIGMA 14 (2018), 032, 1110.4176.
  26. G. Bhatnagar and M. J. Schlosser, Elliptic well-poised Bailey transforms and lemmas on root systems , SIGMA 14 (2018), 025, 1704.00020.
  27. G. Bhatnagar and C. Krattenthaler, The determinant of an elliptic Sylvesteresque matrix, SIGMA 14 (2018), 052, 1802.09885.
  28. A. Borodin, V. Gorin and E. M. Rains, q-Distributions on boxed plane partitions, Selecta Math. 16 (2010), 731-789, 0905.0679.
  29. F. Brünner and V. P. Spiridonov, A duality web of linear quivers, Phys. Lett. B 761 (2016), 261-264, 1605.06991.
  30. F. Brünner and V. P. Spiridonov, 4d N=1 quiver gauge theories and the An Bailey lemma, J. High Energy Phys. 2018, 105, 1712.07018.
  31. F. Brünner, D. Regalado and V. P. Spiridonov, Supersymmetric Casimir energy and SL(3,Z) transformations, J. High Energy Phys. 2017, 041, 1611.03831.
  32. M. Buican, Z. Laczko and T. Nishinaka, N=2 S-duality revisited, J. High Energy Phys. 2017, 087, 1706.03797.
  33. F. van de Bult, Hyperbolic Hypergeometric Functions, PhD thesis, University of Amsterdam, 2007.
  34. F. J. van de Bult, An elliptic hypergeometric integral with W(F4) symmetry, Ramanujan J. 25 (2011), 1-20, 0909.4793.
  35. F. J. van de Bult, Elliptic hypergeometric functions, in D. Levi et al. (eds.), Symmetries and Integrability of Difference Equations, Springer, 2017.
  36. F. J. van de Bult, An elliptic hypergeometric beta integral transformation, 0912.3812.
  37. F. J. van de Bult, Two multivariate quadratic transformations of elliptic hypergeometric integrals, 1109.1123.
  38. F. J. van de Bult, More basic hypergeometric limits of the elliptic hypergeometric beta integral, 1307.2458.
  39. F. J. van de Bult and E. M. Rains, Basic hypergeometric functions as limits of elliptic hypergeometric functions, SIGMA 5 (2009), 059, 0902.0621.
  40. F. J. van de Bult and E. M. Rains, Limits of elliptic hypergeometric biorthogonal functions, J. Approx. Theory 193 (2015), 128-163, 1110.1456.
  41. F. J. van de Bult and E. M. Rains, Limits of multivariate elliptic hypergeometric biorthogonal functions, 1110.1458.
  42. F. J. van de Bult and E. M. Rains, Limits of multivariate elliptic beta integrals and related bilinear forms, 1110.1460.
  43. F. J. van de Bult, E. M. Rains and J. V. Stokman, Properties of generalized univariate hypergeometric functions, Comm. Math. Phys. 275 (2007), 37-95, math/0607250.
  44. H.-Y. Chen and H.-Y. Chen, Heterotic surface defects and dualities from 2d/4d indices, J. High Energy Physic 2014, 4, 1407.4587.
  45. S. H. L. Chen and A. M. Fu, A 4n-point elliptic interpolation formula and its applications, SIAM J. Discrete Math. 31 (2017), 758-765.
  46. D. Chicherin, S. Derkachov, D. Karakhanyan and R. Kirschner, Baxter operators with deformed symmetry, Nuclear Phys. B 868 (2013), 652-683, 1211.2965.
  47. D. Chicherin, S. E. Derkachov and V. P. Spiridonov, New elliptic solutions of the Yang-Baxter equation, Comm. Math. Phys. 345 (2016), 507-543, 1412.3383.
  48. W. Chu, Twisted cubic theta hypergeometric series, Math. Methods Appl. Sci. 44 (2021), 239-252.
  49. W. Chu and C. Jia, Abel's method on summation by parts and theta hypergeometric series, J. Combin. Theory Ser. A 115 (2008), 815-844.
  50. W. Chu and C. Jia, Abel's method on summation by parts for elliptic hypergeometric series, Commun. Contemp. Math. 11 (2009), 337-353.
  51. W. Chu and C. Jia, Quartic theta hypergeometric series, Ramanujan J. 32 (2013), 23-81.
  52. W. Chu and C. Wang, Partial sums of two quartic q-series, SIGMA 5 (2009), 050, 0904.3453 .
  53. H. Coskun, An elliptic BCn Bailey lemma, multiple Rogers-Ramanujan identities and Euler's pentagonal number theorems, Trans. Amer. Math. Soc. 360 (2008), 5397-5433, math/0605653.
  54. H. Coskun and R. A. Gustafson, Well-poised Macdonald functions Wλ and Jackson coefficients ωλ on BCn, in V. B. Kuznetsov and S. Sahi (eds.), Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math. 417, Amer. Math. Soc., Providence, 2006, pp. 127-155, math/0412153.
  55. E. Date, M. Jimbo, A. Kuniba, T. Miwa, and M. Okado, Exactly solvable SOS models. II. Proof of the star-triangle relation and combinatorial identities, in M. Jimbo et al. (eds.), Conformal Field Theory and Solvable Lattice Models, Academic Press, Boston, 1988, pp. 17-122.
  56. R. Y. Denis, S. N. Singh and S. P. Singh, On transformation formulas for theta hypergeometric functions, Ukrainian Math. J. 64 (2012), 1136-1143.
  57. S. Derkachov, D. Karakhanyan and R. Kirschner, Yang-Baxter R-operators and parameter permutations, Nuclear Physics B 785 (2007), 263-285, hep-th/0703076.
  58. S. E. Derkachov, G. A. Sarkissian and V. P. Spiridonov, The elliptic hypergeometric function and 6j-symbols for SL(2,C) group, 2111.06873.
  59. S. E. Derkachov and V. P. Spiridonov, The Yang-Baxter equation, parameter permutations, and the elliptic beta integral, Russian Math. Surveys 68 (2013), 1027-1072, 1205.3520.
  60. S. E. Derkachov and V. P. Spiridonov, Finite dimensional representations of the elliptic modular double, Theoret. and Math. Phys. 183 (2015), 597-618, 1310.7570.
  61. J. F. van Diejen and V. P. Spiridonov, An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums, Math. Res. Lett. 7 (2000), 729-746.
  62. J. F. van Diejen and V. P. Spiridonov, Elliptic Selberg integrals, Internat. Math. Res. Notices 2001 (2001), 1083-1110.
  63. J. F. van Diejen and V. P. Spiridonov, Modular hypergeometric residue sums of elliptic Selberg integrals Lett. Math. Phys. 58 (2001), 223-238.
  64. J. F. van Diejen and V. P. Spiridonov, Elliptic beta integrals and modular hypergeometric sums: an overview, Rocky Mountain J. Math. 32 (2002), 639-656.
  65. J. F. van Diejen and V. P. Spiridonov, Unit circle elliptic beta integrals , Ramanujan J. 10 (2005), 187-204, math/0309279.
  66. T. Dimofte and D. Gaiotto, An E7 surprise, J. High Energy Phys. 2012, 129, 1209.1404.
  67. F. A. Dolan and H. Osborn, Applications of the superconformal index for protected operators and q-hypergeometric identities to N=1 dual theories, Nucl. Phys. B 818 (2009), 137-178, 0801.4947.
  68. F. A. H. Dolan, V. P. Spiridonov and G. S. Vartanov, From 4d superconformal indices to 3d partition functions, Phys. Lett. B 704 (2011), 234-241, 1104.1787.
  69. G. Felder and A. Varchenko, Resonance relations for solutions of the elliptic QKZB equations, fusion rules, and eigenvectors of transfer matrices of restricted interaction-round-a-face models, Commun. Contemp. Math. 1 (1999), 335-403, 9901111.
  70. G. Felder and A. Varchenko, The q-deformed Knizhnik-Zamolodchikov-Bernard heat equation, Comm. Math. Phys. 221 (2001), 549-571, 9809139.
  71. G. Felder and A. Varchenko, Special functions, conformal blocks, Bethe ansatz, and SL(3,Z), Phil. Trans. Roy. Soc. Lond. 359 (2001), 1365-1374, 0101136.
  72. G. Felder and A. Varchenko, q-deformed KZB heat equation: completeness, modular properties and SL(3,Z), Adv. Math. 171 (2002), 228-275, 0110081.
  73. G. Felder and A. Varchenko, Hypergeometric theta functions and elliptic Macdonald polynomials, Internat. Math. Res. Notices 2004, 1037-1055, 0309452.
  74. G. Felder, V. Tarasov and A. Varchenko, Solutions of the elliptic qKZB equations and Bethe ansatz I, in A. Khovanskii et al. (eds.), Topics in Singularity Theory, Amer. Math. Soc., Providence, 1997, pp. 45-75, 9606005.
  75. G. Felder, V. Tarasov and A. Varchenko, Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations, Internat. J. Math. 10 (1999), 943-975, 9705017.
  76. P. J. Forrester and S. O. Warnaar, The importance of the Selberg integral, Bull. Amer. Math. Soc. 45 (2008), 489-534, 0710.3981.
  77. S. Franco, H. Hayashi and A. Uranga, Charting class Sk territory, Phys. Rev. D 92 (2015), 045004, 1504.05988.
  78. I. B. Frenkel and V. G. Turaev, Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions, in V. I. Arnold et al. (eds.), The Arnold-Gelfand Mathematical Seminars, Birkhäuser, Boston, 1997, pp. 171-204.
  79. A. Gadde and S. Gukov, 2d index and surface operators, J. High. Energy Phys. 2014, 80, 1305.0266.
  80. A. Gadde, E. Pomoni, L. Rastelli and S. S. Razamat, S-duality and 2d topological QFT, J. High Energy Phys. 2010, 032, 0910.2225.
  81. A. Gadde, L. Rastelli, S. S. Razamat and W. Yan, The superconformal index of the E6 SCFT, J. High Energy Phys. 2010, 107, 1003.4244.
  82. A. Gadde, L. Rastelli, S. S. Razamat and W. Yan, On the superconformal index of N = 1 IR fixed points: a holographic check, J. High Energy Phys. 2011, 041, 1011.5278.
  83. I. Gahramanov, Mathematical structures behind supersymmetric dualities, Arch. Math. (Brno) 51 (2015), 273-286, 1505.05656.
  84. I. Gahramanov, Superconformal Indices, Dualities and Integrability, PhD thesis, Humboldt-Universität zu Berlin, 2016.
  85. I. Gahramanov, Integrability from supersymmetric duality: a short review, 2201.00351.
  86. I. Gahramanov and S. Jafarzade, Integrable lattice spin models from supersymmetric dualities, 1712.09651.
  87. I. Gahramanov and A. P. Kels, The star-triangle relation, lens partition function, and hypergeometric sum/integrals, J. High Energy Phys. 2017, 040, 1610.09229.
  88. I. Gahramanov and G. Vartanov, Extended global symmetries for 4D N=1 SQCD theories, J. Phys. A. 46 (2013), 285403, 1303.1443.
  89. I. B. Gahramanov and G. S. Vartanov, Superconformal indices and partition functions for supersymmetric field theories, in XVIIth International Congress on Mathematical Physics, World Sci. Publ., Hackensack, 2014, 605-703, 1310.8507.
  90. D. Gaiotto and H.-C. Kim, Surface defects and instanton partition functions, J. High Energy Phys. 2016, 012, 1412.2781.
  91. D. Gaiotto and H.-C. Kim, Duality walls and defects in 5d N=1 theories, J. High Energy Phys. 2017, 019, 1506.03871.
  92. D. Gaiotto, L. Rastelli and S. S. Razamat, Bootstrapping the superconformal index with surface defects, J. High Energy Phys. 2013, 022, 1207.3577.
  93. D. Gaiotto and S. S. Razamat, N=1 theories of class Sk, J. High Energy Phys. 2015, 073, 1503.05159.
  94. I. García-Extebarria, B. Heidenreich and T. Wrase, New N=1 dualities from orientifold transitions - Part I: Field theory, J. High Energy Phys. 2013, 007, 1210.7799.
  95. G. Gasper and M. Rahman, Basic Hypergeometric Series, Second edition, Cambridge University Press, Cambridge, 2004.
  96. G. Gasper and M. J. Schlosser, Summation, transformation, and expansion formulas for multibasic theta hypergeometric series, Adv. Stud. Contemp. Math. (Kyungshang) 11 (2005), 67-84; also published in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 1-17, math/0505215.
  97. M. Hallnäs, E. Langmann, M. Noumi and H. Rosengren, Higher order deformed elliptic Ruijsenaars operators, 2105.02536 .
  98. Q.-H. Hou and Y. Wei, Telescoping method, summation formulas, and inversion pairs, Electron. Res. Arch. 29 (2021), 2657–2671.
  99. N. Hoshi, M. Katori, T. H. Koornwinder and M. J. Schlosser, On an identity of Chaundy and Bullard. III. Basic and elliptic extensions, 2304.10003.
  100. M. Ito and M. Noumi, Derivation of a BCn elliptic summation formula via the fundamental invariants, Constr. Approx. 45 (2017), 33-46, 1504.07108.
  101. M. Ito and M. Noumi, Evaluation of the BCn elliptic Selberg integrals via the fundamental invariants, Proc. Amer. Math. Soc. 145 (2017), 689-703, 1504.07317.
  102. M. Ito and M. Noumi, Elliptic extension of Gustafson's q-integral of type G2, 1902.04858.
  103. M. Ito and M. Noumi, A determinant formula associated with the elliptic hypergeometric integrals of type BCn, 1902.10533.
  104. Y. Kajihara, Symmetry groups of An hypergeometric series, SIGMA 10 (2014), 026, 1310.7273.
  105. Y. Kajihara and M. Noumi, Multiple elliptic hypergeometric series. An approach from the Cauchy determinant, Indag. Math. 14 (2003), 395-421, math/0306219.
  106. K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta and Y. Yamada, 10E9 solution to the elliptic Painlevé equation, J. Phys. A 36 (2003), L263-L272, nlin/0303032.
  107. K. Kashaev, F. Luo and G. Vartanov, A TQFT of Turaev-Viro type on shaped triangulations, Ann. Henri Poincaré 17 (2016),1109-1143, 1210.8393.
  108. A. P. Kels, New solutions of the star-triangle relation with discrete and continuous spin variables, J. Phys. A 48 (2015), 435201, 1504.07074.
  109. A. P. Kels, Two-component Yang-Baxter maps associated to integrable quad equations, 1910.03562.
  110. A. P. Kels and M. Yamazaki, Elliptic hypergeometric sum/integral transformations and supersymmetric lens index, SIGMA 14 (2018), 013, 1704.03159.
  111. A. P. Kels and M. Yamazaki, Lens generalization of τ-functions for the elliptic discrete Painlevé equation, 1810.12103.
  112. E. Koelink and Y. van Norden, Pairings and actions for dynamical quantum groups, Adv. Math. 208 (2007), 1-39, math/0412205.
  113. E. Koelink, Y. van Norden, and H. Rosengren, Elliptic U(2) quantum group and elliptic hypergeometric series, Comm. Math. Phys. 245 (2004), 519-537, math/0304189.
  114. Y. Komori, Elliptic Ruijsenaars operators and elliptic hypergeometric integrals, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 49-56.
  115. Y. Komori, Y. Masuda and M. Noumi, Duality transformation formulas for multiple elliptic hypergeometric series of type BC, Constr. Approx. 44 (2016), 483-516, 1410.6921.
  116. H. Konno, The vertex-face correspondence and the elliptic 6j-symbols , Lett. Math. Phys. 72 (2005), 243-258, math/0503725.
  117. H. Konno, Generalized elliptic 6j-symbols in terms of the vertex-face intertwining vectors, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 57-69.
  118. H. Konno, Elliptic quantum group Uq,p(\hat{sl}2), Hopf algebroid structure and elliptic hypergeometric series, J. Geom. Phys. 59 (2009), 1485-1511, 0803.2292.
  119. H. Konno, Elliptic Quantum Groups, Springer, 2020.
  120. A. Korovnichenko, V. P. Spiridonov and A. S. Zhedanov, Poisson algebras on elliptic curves, Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos. 50 (2004), 1116-1123 (or 1116-1125?).
  121. C. Krattenthaler and M. J. Schlosser, The major index generating function of standard Young tableaux of shapes of the form "staircase minus rectangle", in K. Alladi et al. (eds.), Ramanujan 125, Contemp. Math. 627, Amer. Math. Soc., Providence, 2014, pp. 111-122, 1402.4538.
  122. D. I. Krotkov and V. P. Spiridonov, Infinite elliptic hypergeometric series: convergence and difference equations, 2307.08002.
  123. J. Küstner, M. J. Schlosser and M. Yoo, Lattice paths and negatively indexed weight-dependent binomial coefficients, 2204.05505.
  124. D. Kutasov and J. Lin, N=1 Duality and the Superconformal Index, 1402.5411.
  125. R. Langer, M. J. Schlosser and S. O. Warnaar, Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture, SIGMA 5 (2009), 055, 0905.4033.
  126. C.-H. Lee, E. M. Rains and S. O. Warnaar, An elliptic hypergeometric function approach to branching rules, 2007.03174.
  127. K. Y. Magadov and V. P. Spiridonov, Matrix Bailey lemma and the star-triangle relation, SIGMA 14 (2018), 121, 1810.10806.
  128. A. P. Magnus, Elliptic hypergeometric solutions to elliptic difference equations, SIGMA 5 (2009), 038, 0903.4803.
  129. K. Maruyoshi and J. Yagi, Surface defects as transfer matrices, Prog. Theor. Exp. Phys. 2016, 113B01, 1606.01041.
  130. B. Nazzal and S. S. Razamat, Surface defects in E-string compactifications and the van Diejen model, SIGMA 14 (2018), 036, 1801.00960.
  131. V. Niarchos, Seiberg dualities and the 3d/4d connection, J. High Energy Phys. 2012, 75, 1205.2086.
  132. F. Nieri, An elliptic Virasoro symmetry in 6d, Lett. Math. Phys. 107 (2017), 2147-2187, 1511.00574.
  133. F. Nieri and S. Pasquetti, Factorisation and holomorphic blocks in 4d, J. High Energy Phys. 2015, 155, 1507.00261.
  134. Y. van Norden, Dynamical Quantum Groups, Duality and Special Functions, PhD thesis, Delft University of Technology, 2005.
  135. M. Noumi, Padé interpolation and hypergeometric series, in A. Dzhamay, K. Maruno and C. M. Ormerod (eds.), Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, Contemp. Math. 651, Amer. Math. Soc., Providence, 2015, pp. 1-23. 1503.02147.
  136. M. Noumi, Remarks on τ-functions for the difference Painlevé equations of type E8, in H. Konno et al. (eds.), Representation Theory, Special Functions and Painlevé Equations, Math. Soc. Japan, Tokyo, 2018, pp. 1-65, 1604.06869.
  137. M. Noumi and A. Sano, An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A, 2012.03135.
  138. M. Noumi, S. Tsujimoto and Y. Yamada, Padé interpolation for elliptic Painlevé equation, in K. Iohara et al. (eds.), Symmetries, Integrable Systems and Representations, Springer-Verlag, London, 2013, pp. 463-482, 1204.0294.
  139. W. Peelaers, Higgs branch localization of N=1 theories on S3 x S1, J. High. Energy Phys. 2014, 30, 1403.2711.
  140. E. M. Rains, Recurrences for elliptic hypergeometric integrals, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 183-199, math/0504285.
  141. E. M. Rains, BCn-symmetric abelian functions, Duke Math. J. 135 (2006), 99-180, math/0402113.
  142. E. M. Rains, Limits of elliptic hypergeometric integrals, Ramanujan J. 18 (2009), 257-306, math/0607093.
  143. E. M. Rains, Transformations of elliptic hypergeometric integrals, Ann. Math. 171 (2010), 169-243, math/0309252.
  144. E. M. Rains, Elliptic analogues of the Macdonald and Koornwinder polynomials, in Proceedings of the International Congress of Mathematicians, Vol. IV, Hindustan Book Agency, New Delhi, 2010, pp. 2530-2554.
  145. E. M. Rains, An isomonodromy interpretation of the hypergeometric solution of the elliptic Painlevé equation (and generalizations), SIGMA 7 (2011), 088, 0807.0258.
  146. E. M. Rains, Elliptic Littlewood identities, J. Combin. Theory A 119 (2012), 1558-1609, 0806.0871.
  147. E. M. Rains, Generalized Hitchin systems on rational surfaces, 1307.4033.
  148. E. M. Rains, Multivariate quadratic transformations and the interpolation kernel, SIGMA 14 (2018), 019, 1408.0305.
  149. E. M. Rains, The noncommutative geometry of elliptic difference equations, 1607.08876.
  150. E. M. Rains and V. P. Spiridonov, Determinants of elliptic hypergeometric integrals, Func. Anal. Appl. 43 (2009), 297-311, 0712.4253.
  151. E. M. Rains, Y. Sun and A. Varchenko, Affine Macdonald conjectures and special values of Felder-Varchenko functions, Selecta Math. 24 (2018), 1549-1591, 1610.01917.
  152. L. Rastelli and S. S. Razamat, The superconformal index of theories of class S, in J. Teschner (ed.), New Dualities of Supersymmetric Gauge Theories, Springer, Cham, 2016, pp. 261-305, 1412.7131.
  153. L. Rastelli and S. S. Razamat, The supersymmetric index in four dimensions, J. Phys. A 50 (2017), 443013, 1608.02965.
  154. S. S. Razamat, On the N=2 superconformal index and eigenfunctions of the elliptic RS model, Lett. Math. Phys. 104 (2014), 673-690, 1309.0278.
  155. S. S. Razamat, Flavored surface defects in 4d N=1 SCFTs, 1808.09509.
  156. S. S. Razamat, C. Vafa and G. Zafrir, 4d N=1 from 6d (1,0), J. High Energy Phys. 2017, 064, 1610.09178.
  157. S. S. Razamat and B. Willett, Global properties of supersymmetric theories and the lens space, Comm. Math. Phys. 334 (2015), no. 2, 661-696, 1307.4381.
  158. H. Rosengren, A proof of a multivariable elliptic summation formula conjectured by Warnaar, in B. C. Berndt and K. Ono (eds.), q-Series with Applications to Combinatorics, Number Theory, and Physics, Contemp. Math. 291, Amer. Math. Soc., Providence, 2001, pp. 193-202, math/0101073.
  159. H. Rosengren, Elliptic hypergeometric series on root systems, Adv. Math. 181 (2004), 417-447, math/0207046.
  160. H. Rosengren, Sklyanin invariant integration, Int. Math. Res. Not. 2004 (2004), 3207-3232, math/0405072.
  161. H. Rosengren, An elliptic determinant transformation, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 241-246, math/0505248.
  162. H. Rosengren, New transformations for elliptic hypergeometric series on the root system An, Ramanujan J. 12 (2006), 155-166, math/0305379.
  163. H. Rosengren, An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic), Ramanujan J. 13 (2007), 133-168, math/0312310.
  164. H. Rosengren, Felder's elliptic quantum group and elliptic hypergeometric series on the root system An, Int. Math. Res. Not. 2011 (2011), 2861-2920, 1003.3730.
  165. H. Rosengren, Elliptic hypergeometric functions, in H. S. Cohl and M. E. H. Ismail (eds.), Lectures on Orthogonal Polynomials and Special Functions, Cambridge University Press, to appear, 1608.06161.
  166. H. Rosengren, Gustafson-Rakha-type elliptic hypergeometric series, SIGMA 13 (2017), 037, 1701.08960.
  167. H. Rosengren and M. J. Schlosser, Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations, Indag. Math. 14 (2003), 483-514, math/0304249.
  168. H. Rosengren and M. J. Schlosser, On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series, J. Comput. Appl. Math. 178 (2005), 377-391, math/0309358.
  169. H. Rosengren and M. J. Schlosser, Multidimensional matrix inversions and elliptic hypergeometric series on root systems, SIGMA 16 (2020), 088, 2005.02203.
  170. H. Rosengren and S. O. Warnaar, Elliptic hypergeometric functions associated with root systems, in T. H. Koornwinder and J. V. Stokman (eds.), Multivariable Special Functions, Cambridge University Press, to appear, 1704.08406.
  171. G. Sarkissian and V. P. Spiridonov, From rarefied elliptic beta integral to parafermionic star-triangle relation, 1809.00493.
  172. G. Sarkissian and V. P. Spiridonov, The endless beta integrals, 2005.01059.
  173. G. A. Sarkissian and V. P. Spiridonov, Complex hypergeometric functions and integrable many body problems, 2105.15031.
  174. G. A. Sarkissian and V. P. Spiridonov, Elliptic and complex hypergeometric integrals in quantum field theory, Physics of Particles and Nuclei Letters 20 (2023), 281-286.
  175. M. J. Schlosser, Elliptic enumeration of nonintersecting lattice paths, J. Combin. Theory A 114 (2007), 505-521, math/0602260.
  176. M. J. Schlosser, A Taylor expansion theorem for an elliptic extension of the Askey-Wilson operator, in D. Dominici and R. S. Maier (eds.), Special Functions and Orthogonal Polynomials, Contemp. Math. 471, Amer. Math. Soc., Providence, 2008, pp. 175-186, 0803.2329.
  177. M. J. Schlosser, A noncommutative weight-dependent generalization of the binomial theorem, 1106.2112.
  178. M. J. Schlosser, An elliptic extension of the multinomial theorem, 2307.12921.
  179. M. J. Schlosser and M. Yoo, Elliptic hypergeometric summations by Taylor series expansion and interpolation, SIGMA 12 (2016), 039, 1602.09027.
  180. S. P. Singh and A. K. Singh, On a transformation formula for elliptic hypergeometric series, South East Asian J. Math. Math. Sci. 10 (2011), 79-88.
  181. V. P. Spiridonov, Solitons and Coulomb plasmas, similarity reductions and special functions, in C. Dunkl et al. (eds.), Special Functions, World Scientific, River Edge, 2000, pp. 324-338.
  182. V. P. Spiridonov, On the elliptic beta function, Russian Math. Surveys 56 (2001), 185-186.
  183. V. P. Spiridonov, New special functions of hypergeometric type and elliptic beta integrals (in Russian), Phys. Part. Nucl. 32 (2001), 88--92.
  184. V. P. Spiridonov, Elliptic beta integrals and special functions of hypergeometric type, in G. von Gehlen and S. Pakuliak (eds.), Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, Kluwer, Dordrecht, 2001, pp. 305-313.
  185. V. P. Spiridonov, Theta hypergeometric series, in V.A. Malyshev and A.M. Vershik (eds.), Asymptotic Combinatorics with Applications to Mathematical Physics, Kluwer, Dordrecht, 2002, pp. 307-327, math/0303204.
  186. V. P. Spiridonov, An elliptic beta integral, in S. Elaydi et al. (eds.), New Trends in Difference Equations, Taylor & Francis, London, 2002, pp. 273-282.
  187. V. P. Spiridonov, An elliptic incarnation of the Bailey chain, Int. Math. Res. Not. 2002 (2002), 1945-1977.
  188. V. P. Spiridonov, Modularity and total ellipticity of some multiple series of hypergeometric type, Theor. Math. Phys. 135 (2003), 836-848.
  189. V. P. Spiridonov, Theta hypergeometric integrals, St. Petersburg Math. J. 15 (2004), 929-967, math/0303205.
  190. V. P. Spiridonov, A Bailey tree for integrals, Theor. Math. Phys. 139 (2004), 536-541, math/0312502.
  191. V. P. Spiridonov, Elliptic Hypergeometric Functions (in Russian), Habilitation Thesis, JINR, Dubna, 2004, 1610.01557.
  192. V. P. Spiridonov, Classical elliptic hypergeometric functions and their applications, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 253-287, math/0511579.
  193. V. P. Spiridonov, A multiparameter summation formula for Riemann theta functions, in V. B. Kuznetsov and S. Sahi (eds.), Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math. 417, Amer. Math. Soc., Providence, 2006, pp. 345-353, math/0408366.
  194. V. P. Spiridonov, Short proofs of the elliptic beta integrals, Ramanujan J. 13 (2007), 265-283, math/0408369.
  195. V. P. Spiridonov, Elliptic hypergeometric functions and Calogero-Sutherland-type models, Theor. Math. Phys 150 (2007), 266-277.
  196. V. P. Spiridonov, An elliptic analogue of the Gauss hypergeometric function, preprint, MPIM2007-75 (2007).
  197. V. P. Spiridonov, Essays on the theory of elliptic hypergeometric functions, Russian Math. Surveys 63 (2008), 405-472, 0805.3135.
  198. V. P. Spiridonov, Continuous biorthogonality of the elliptic hypergeometric function, St. Petersburg Math. J. 20 (2009), 791-812, 0801.4137.
  199. V. P. Spiridonov, Elliptic hypergeometric terms, SNF Séminaire et Congrès 23 (2011), 385-405, 1003.4491.
  200. V. P. Spiridonov, Elliptic beta integrals and solvable models of statistical mechanics, in P. B. Acosta-Humánez et al. (eds.), Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemp. Math. 563, Amer. Math. Soc., Providence, 2012, pp. 345-353, 1011.3798.
  201. V. P. Spiridonov, Aspects of elliptic hypergeometric functions, in B. C. Berndt and D. Prasad (eds.), The legacy of Srinivasa Ramanujan, Ramanujan Math. Soc., Mysore, 2013, pp. 347-361, 1307.2876.
  202. V. P. Spiridonov, Modified elliptic gamma functions and 6d superconformal indices, Lett. Math. Phys. 104 (2014), 397-414, 1211.2703.
  203. V. P. Spiridonov, Elliptic hypergeometric functions, complement to the Russian edition of G. E. Andrews, R. Askey, and R. Roy, Special Functions, 0704.3099.
  204. V. P. Spiridonov, Rarefied elliptic hypergeometric functions, Adv. Math. 331 (2018), 830–873, 1609.00715.
  205. V. P. Spiridonov, The rarefied elliptic Bailey lemma and the Yang-Baxter equation, 1904.12046.
  206. V. P. Spiridonov, Superconformal indices, Seiberg dualities and special functions, Phys. Particles Nuclei 51 (2020), 508-513, arXiv:1912.11514.
  207. V. P. Spiridonov, Introduction to the theory of elliptic hypergeometric integrals, arXiv:1912.12971.
  208. V. P. Spiridonov and G. S. Vartanov, Superconformal indices for N=1 theories with multiple duals, Nucl. Phys.B 824 (2010), 192-216, 0811.1909.
  209. V. P. Spiridonov and G. S. Vartanov, Supersymmetric dualities beyond the conformal window, Phys. Rev. Lett. 105 (2010), 061603, 1003.6109.
  210. V. P. Spiridonov and G. S. Vartanov, Elliptic hypergeometry of supersymmetric dualities, Comm. Math. Phys. 304 (2011), 797-874, 0910.5944.
  211. V. P. Spiridonov and G. S. Vartanov, Superconformal indices of N=4 dual field theories, Lett. Math. Phys. 100 (2012), 97-118, 1005.4196.
  212. V. P. Spiridonov and G. S. Vartanov, Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions, J. High Energy Phys. 2012, 016, 1203.5677.
  213. V. P. Spiridonov and G. S. Vartanov, Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices, Comm. Math. Phys. 325 (2014), 421-486, 1107.5788.
  214. V. P. Spiridonov and G. S. Vartanov, Vanishing superconformal indices and the chiral symmetry breaking, 1402.2312.
  215. V. P. Spiridonov and S. O. Warnaar, Inversions of integral operators and elliptic beta integrals on root systems, Adv. Math. 207 (2006), 91-132, math/0411044.
  216. V. P. Spiridonov and S. O. Warnaar, New multiple 6ψ6 summation formulas and related conjectures, Ramanujan J. 25 (2011), 319-342.
  217. V. P. Spiridonov and A. S. Zhedanov, Classical biorthogonal rational functions on elliptic grids, C. R. Math. Acad. Sci. Soc. R. Can. 22 (2000), 70-76.
  218. V. P. Spiridonov and A. S. Zhedanov, Spectral transformation chains and some new biorthogonal rational functions, Comm. Math. Phys. 210 (2000), 49-83.
  219. V. P. Spiridonov and A. S. Zhedanov, Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids, in J. Bustoz et al. (eds.), Special Functions 2000: Current Perspective and Future Directions, Kluwer, Dordrecht, 2001, pp. 365-388.
  220. V. P. Spiridonov and A. S. Zhedanov, To the theory of biorthogonal rational functions (in Japanese), Surikaisekikenkyusho Kokyuroku 1302 (2003), 172-192.
  221. V. P. Spiridonov and A. S. Zhedanov, Poisson algebras for some generalized eigenvalue problems, J. Phys. A 37 (2004), 10429-10443.
  222. V. P. Spiridonov and A. S. Zhedanov, Elliptic grids, rational functions, and the Padé interpolation, Ramanujan J. 13 (2007), 285-310.
  223. J. V. Stokman, Hyperbolic beta integrals, Adv. Math. 190 (2005), 119-160, math/0303178.
  224. M. Sudano, The Römelsberger index, Berkooz deconfinement, and infinite families of Seiberg duals, J. High Energy Phys. 2012, 051, 1112.2996.
  225. Y. Sun, Traces of intertwiners for quantum affine sl2 and Felder-Varchenko functions, Comm. Math. Phys. 347 (2016), 573-653, 1508.03918.
  226. J. Teschner and G. S. Vartanov, 6j-symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories, Lett. Math. Phys. 104 (2014), 527-551, 1202.4698.
  227. S. Tsujimoto and A. Zhedanov, Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle, SIGMA 5 (2009), 033, 0809.2574.
  228. G. S. Vartanov, On the ISS model of dynamical SUSY breaking, Phys. Lett. B 696 (2011), 288-290, 1009.2153.
  229. J. Wang and X. Ma, Further study on elliptic interpolation formulas for the elliptic Askey-Wilson polynomials and allied identities, 2008.05636.
  230. S. O. Warnaar, Summation and transformation formulas for elliptic hypergeometric series, Constr. Approx. 18 (2002), 479-502, math/0001006.
  231. S. O. Warnaar, Extensions of the well-poised and elliptic well-poised Bailey lemma, Indag. Math. 14 (2003), 571-588, math/0309241.
  232. S. O. Warnaar, Summation formulae for elliptic hypergeometric series, Proc. Amer. Math. Soc. 133 (2005), 519-527, math/0309242.
  233. J. Yagi, Quiver gauge theories and integrable lattice models, J. High Energy Phys. 2015, 065, 1504.04055.
  234. J. Yagi, Branes and integrable lattice models, Modern Phys. Lett. A 32 (2017), 1730003, 1610.05584.
  235. J. Yagi, Surface defects and elliptic quantum groups, J. High Energy Phys. (2017), 013, 1701.05562.
  236. Y. Yamada, An elliptic Garnier system from interpolation, SIGMA 13 (2017), 069, 1706.05155.
  237. M. Yamazaki, Quivers, YBE and 3-manifolds, J. High Energy Phys. 2012, 147, 1203.5784.
  238. M. Yamazaki, Four-dimensional superconformal index reloaded, Theoret. and Math. Phys. 174 (2013), 154-166.
  239. M. Yamazaki, New integrable models from the gauge/YBE correspondence, J. Stat. Phys. 154 (2014), 895–911, 1307.1128.
  240. Y. Yoshida, Factorization of 4d N=1 superconformal index, 1403.0891.
  241. A. Zabrodin, Commuting difference operators with elliptic coefficients from Baxter's vacuum vectors, J. Phys. A 33 (2000), 3825-3850, math/9912218.
  242. A. Zabrodin, Intertwining operators for Sklyanin algebra and elliptic hypergeometric series, J. Geom. Phys. 61 (2011), 1733-1754, 1012.1228.
  243. Z. Zhang and J. Huang, The Cn WP-Bailey chain, Acta Math. Sci. Ser. B (Engl. Ed.) 38 (2018), 1789-1804.
  244. T. Zhao and X. Deng, A matrix inverse pair and elliptic hypergeometric summations, Int. J. Nonlinear Sci. 22 (2016), 93-99.
  245. A. S. Zhedanov, Padé interpolation table and biorthogonal rational functions, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 323-363.
  246. A. Zhedanov, Elliptic polynomials orthogonal on the unit circle with a dense point spectrum, Ramanujan J. 19 (2009), 351-384, 0711.4696.
  247. A. S. Zhedanov and V. P. Spiridonov, A terminating elliptic hypergeometric continued fraction (in Russian), Chebyshevskii Sb. 7 (2006), 81-100.
  248. B. I. Zwiebel, Charging the superconformal index, J. High Energy Phys. 2012, 116, 1111.1773.