Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 014, 11 pages      math.CA/0701677      http://dx.doi.org/10.3842/SIGMA.2007.014
Contribution to the Vadim Kuznetsov Memorial Issue

An Analytic Formula for the A2 Jack Polynomials

Vladimir V. Mangazeev
Department of Theoretical Physics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, Australia

Received November 01, 2006, in final form January 05, 2007; Published online January 24, 2007

Abstract
In this letter I shall review my joint results with Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14 (2003), 451-482] on separation of variables (SoV) for the An Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995), 27-34] where the integral representations for the A2 Jack polynomials was derived. Using special polynomial bases I shall obtain a more explicit expression for the A2 Jack polynomials in terms of generalised hypergeometric functions.

Key words: Jack polynomials; integral operators; hypergeometric functions.

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