An Analytic Formula for the A_2 Jack Polynomials

Vladimir V. Mangazeev

doi:10.3842/SIGMA.2007.014

paper

An Analytic Formula for the A_2 Jack Polynomials

arXiv:math/0701677 · doi:10.3842/SIGMA.2007.014

Abstract

In this letter I shall review my joint results with Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14 (2003), 451-482, math.CA/0306242] on separation of variables for the $A_{n}$ Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995), 27-34, solv-int/9508002] where the integral representations for the $A_{2}$ Jack polynomials was derived. Using special polynomial bases I shall obtain a more explicit expression for the $A_{2}$ Jack polynomials in terms of generalised hypergeometric functions.

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/