Separation of variables in the $A_2$ type Jack polynomials

V. B. Kuznetsov; E. K. Sklyanin

paper

Separation of variables in the $A_{2}$ type Jack polynomials

arXiv:solv-int/9508002

Abstract

An integral operator $M$ is constructed performing a separation of variables for the 3-particle quantum Calogero-Sutherland (CS) model. Under the action of $M$ the CS eigenfunctions (Jack polynomials for the root system $A_{2}$ ) are transformed to the factorized form $ϕ (y_{1}) ϕ (y_{2})$ , where $ϕ (y)$ is a trigonometric polynomial of one variable expressed in terms of the $_{3} F_{2}$ hypergeometric series. The inversion of $M$ produces a new integral representation for the $A_{2}$ Jack polynomials.

17 pages, LATEX, macros included, no figures

References in corpus (1)

Quantum Inverse Scattering Method. Selected Topics

Separation of variables in the A2​ type Jack polynomials

Abstract

References in corpus (1)

Cited by in corpus (2)

Separation of variables in the $A_{2}$ type Jack polynomials