Martin Hallnäs

Department of Mathematical Sciences
Chalmers University of Technology and the University of Gothenburg
SE-412 96 Gothenburg
Sweden

Office: H4027 in the MV-building
E-mail: hallnas at chalmers.se
Phone: +46 (0)31 7723536


Research Interests

Quantum integrable systems and special functions, in particular integrable (quantum) many-body systems of Calogero-Moser-Sutherland and Ruijsenaars-Schneider type, Jack and Macdonald symmetric functions and hypergeometric functions associated with root systems, as well as their interrelations. I am a member of the Mathematical Physics group in the Department of Mathematical Sciences at Chalmers University of Technology and the University of Gothenburg. The following presentations explain some of my recent and ongoing research projects:

Editorial activities: Subject editor in Mathematical Physics for Glasgow Mathematical Journal.

Master Thesis Projects: Happy to discuss possible topics for a master thesis in mathematical physics, integrable systems or a related area.

Pre-prints

My pre-prints, old and new, are all available on the arXiv, with direct links to unpublished ones given below.

  1. New orthogonality relations for super-Jack polynomials and an associated Lassalle-Nekrasov correspondence
    arXiv:2203.14605
  2. (w/ E. Langmann, M. Noumi and H. Rosengren) Higher order deformed elliptic Ruijsenaars operators
    arXiv:2105.02536

Publications

Reviews of most of my published papers can be found on MathSciNet and on Zentralblatt der Mathematik. Below you can find a complete list of my published papers, with direct links to the relevant journal.

  1. (w/ E. Langmann, M. Noumi and H. Rosengren) From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators
    Selecta Math. (N.S.) (2022)
    https://doi.org/10.1007/s00029-021-00745-z
  2. (w/ F. Atai and E. Langmann) Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
    Comm. Math. Phys. (2021)
    doi:10.1007/s00220-021-04166-z
  3. (w/ M. V. Feigin and A. P. Veselov) Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence
    Comm. Math. Phys. (2021)
    doi:10.1007/s00220-021-04036-8
  4. (w/ S. Ruijsenaars) Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. III. Factorized asymptotics
    Int. Math. Res. Not. IMRN 2021
    doi:10.1093/imrn/rnaa193
  5. (w/ F. Atai and E. Langmann) Orthogonality of super-Jack polynomials and a Hilbert space interpretation of deformed Calogero-Moser-Sutherland operators
    Bull. London Math. Soc. 51 (2019)
    doi:10.1112/blms.12234
  6. (w/ T. F. Görbe) Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars-Schneider systems
    J. Integrable Syst. 3 (2018)
    doi:10.1093/integr/xyy015
  7. (w/ S. Ruijsenaars) Joint eigenfunctions for the relativistic Calogero–Moser Hamiltonians of hyperbolic type II. The two- and three-variable cases
    Int. Math. Res. Not. IMRN 2018
    doi:10.1093/imrn/rnx020
  8. (w/ S. Ruijsenaars) Product formulas for the relativistic and nonrelativistic conical functions
    Advanced Studies in Pure Mathematics 76 (2018)
    doi:10.1142/e057
  9. (w/ W. A. Haese-Hill and A. P. Veselov) On the spectra of real and complex Lamé operators
    SIGMA Symmetry Integrability Geom. Methods Appl. 13 (2017)
    doi:10.3842/SIGMA.2017.049
  10. (w/ W. A. Haese-Hill and A. P. Veselov) Complex exceptional orthogonal polynomials and quasi-invariance
    Lett. Math. Phys. 106 (2016)
    doi:10.1007/s11005-016-0828-8
  11. (w/ S. Ruijsenaars) A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians
    Int. Math. Res. Not. IMRN 2015
    doi:10.1093/imrn/rnu267
  12. (w/ E. Langmann) A product formula for the eigenfunctions of a quartic oscillator
    J. Math. Anal. Appl. 426 (2015)
    doi:10.1016/j.jmaa.2015.02.014
  13. (w/ S. Ruijsenaars) Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type: I. First steps
    Int. Math. Res. Not. IMRN 2014
    doi:10.1093/imrn/rnt076.
  14. (w/ F. Atai and E. Langmann) Source identities and kernel functions for deformed (quantum) Ruijsenaars models
    Lett. Math. Phys. 104 (2014)
    doi:10.1007/s11005-014-0690-5
  15. (w/ M. V. Feigin and A. P. Veselov) Baker-Akhiezer functions and generalised Macdonald-Mehta integrals
    J. Math. Phys. 54 (2013)
    doi:10.1063/1.4804615
  16. (w/ S. Ruijsenaars) Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems
    J. Math. Phys. 53 (2012)
    doi:10.1063/1.4764878
  17. (w/ P. Desrosiers) Hermite and Laguerre symmetric functions associated with operators of Calogero-Moser-Sutherland type
    SIGMA Symmetry Integrability Geom. Methods Appl. 8 (2012)
    doi:10.3842/SIGMA.2012.049
  18. An orthogonality relation for multivariable Bessel polynomials
    Integral Transforms Spec. Funct. 21 (2010)
    doi:10.1080/10652460903211312
  19. (w/ E. Langmann) A unified construction of generalized classical polynomials associated with operators of Calogero-Sutherland type
    Constr. Approx. 31 (2010)
    doi:10.1007/s00365-009-9060-4
  20. Multivariable Bessel polynomials related to the hyperbolic Sutherland model with external Morse potential
    Int. Math. Res. Not. IMRN 2009
    doi:10.1093/imrn/rnn167
  21. An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models
    SIGMA Symmetry Integrability Geom. Methods Appl. 3 (2007)
    doi:10.3842/SIGMA.2007.037
  22. (w/ E. Langmann) Explicit formulae for the eigenfunctions of the N-body Calogero model
    J. Phys. A 39 (2006)
    doi:10.1088/0305-4470/39/14/002
  23. (w/ E. Langmann and C. Paufler) Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles
    J. Phys. A 38 (2005)
    doi:10.1088/0305-4470/38/22/018
  24. (w/ E. Langmann) Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line
    J. Math. Phys. 46 (2005)
    doi:10.1063/1.1865320

Last updated: 31 March 2022