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

V Kuznetsov; Evgeni Sklyanin

doi:10.1088/0305-4470/29/11/014

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

V Kuznetsov, Evgeni Sklyanin

Mathematics

Research output: Contribution to journal › Article › peer-review

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 ) into the factorized form where S(y) is a Laurent polynomial of one variable expressed in terms of the basic hypergeometric series. The inversion of M produces a new integral representation for the Macdonald polynomials. We also present some results and conjectures for the general n-particle case

Original language	English
Pages (from-to)	2779-2804
Number of pages	26
Journal	Journal of Physics A: Mathematical and General
Volume	29
Issue number	11
DOIs	https://doi.org/10.1088/0305-4470/29/11/014
Publication status	Published - Jun 1996

Keywords

mathematical physics;

Access to Document

10.1088/0305-4470/29/11/014

http://arxiv.org/abs/q-alg/9602023

Cite this

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title = "Separation of variables for A2 Ruijsenaars model and new integral representation for A2 Macdonald polynomials",

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 ) into the factorized form where S(y) is a Laurent polynomial of one variable expressed in terms of the basic hypergeometric series. The inversion of M produces a new integral representation for the Macdonald polynomials. We also present some results and conjectures for the general n-particle case",

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T1 - Separation of variables for A2 Ruijsenaars model and new integral representation for A2 Macdonald polynomials

AU - Kuznetsov, V

AU - Sklyanin, Evgeni

PY - 1996/6

Y1 - 1996/6

N2 - 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 ) into the factorized form where S(y) is a Laurent polynomial of one variable expressed in terms of the basic hypergeometric series. The inversion of M produces a new integral representation for the Macdonald polynomials. We also present some results and conjectures for the general n-particle case

AB - 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 ) into the factorized form where S(y) is a Laurent polynomial of one variable expressed in terms of the basic hypergeometric series. The inversion of M produces a new integral representation for the Macdonald polynomials. We also present some results and conjectures for the general n-particle case

KW - mathematical physics;

U2 - 10.1088/0305-4470/29/11/014

DO - 10.1088/0305-4470/29/11/014

M3 - Article

SN - 0305-4470

VL - 29

SP - 2779

EP - 2804

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 11

ER -