Macdonald's polynomials and representations of quantum groups

Details Macdonald's polynomials and representations of quantum groups Macdonald's polynomials and representations of quantum groups

1993-12-13

arxiv.org/abs/hep-th/9312103v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, no figures

Scientific paper

In this paper we present a formula for Macdonald's polynomials for the root system A(n-1) which arises from the representation theory of quantum sl(n). This formula expresses Macdonald's polynomials via (weighted) traces of intertwining operators between certain modules over quantum sl(n). We also describe the commutative system of Macdonald's difference operators using the generators of the center of the quantum universal enveloping algebra, and use this description to prove a trace formula for generic eigenfunctions of these operators. These functions are generalized q-hypergeometric functions which are related to solutions of the quantum Knizhnik-Zamolodchikov equations.

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