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Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models

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Abstract

We consider the relativistic generalization of the quantum A N-1 Calogero–Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh–Feigin–Veselov–Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.

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Authors and Affiliations

  1. Department of Theoretical Physics, KTH Royal Institute of Technology, 106 91, Stockholm, Sweden

    Farrokh Atai & Edwin Langmann

  2. Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU, UK

    Martin Hallnäs

Authors
  1. Farrokh Atai
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  2. Martin Hallnäs
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  3. Edwin Langmann
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Correspondence to Edwin Langmann.

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Atai, F., Hallnäs, M. & Langmann, E. Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models. Lett Math Phys 104, 811–835 (2014). https://doi.org/10.1007/s11005-014-0690-5

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  • DOI: https://doi.org/10.1007/s11005-014-0690-5

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