Separation of variables for the A2 Ruijsenaars model and a new integral representation for the A2 Macdonald polynomials.

Vadim b Kuzentsov, E.K. Sklyanin

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    Abstract

    Using the Baker-Akhiezer function technique we construct a separation of variables for the classical trigonometric three-particle Ruijsenaars model (a relativistic generalization of the Calogero-Moser-Sutherland model). In the quantum case, an integral operator M is constructed from the Askey-Wilson contour integral. The operator M transforms the eigenfunctions of the commuting Hamiltonians (the Macdonald polynomials for the root sytem A2) into the factorized form S(y1)S(y2) where S(y) is a Laurent polynomial of one variable expressed in terms of the 3φ2(y) basic hypergeometric series. The inversion of M produces a new integral representation for the A2 Macdonald polynomials. We also present some results and conjectures for the general n-particle case.
    Original languageEnglish
    JournalJournal of Physics A: Mathematical and General
    Volume29
    Issue number11
    Pages (from-to)2779-2804
    ISSN0305-4470
    DOIs
    Publication statusPublished - 1996

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