# Macdonald polynomials and quantum gl(n)

## ABSTRACT

I will give an elementary introduction to the theory of Macdonald polynomials (for a root system of type A), and then explain my work with A.Kirillov Jr. (1994) where this theory is connected with representation theory of the quantum group U_q(gl(n)). This allows to obtain a representation theoretic interpretation of all the main identities with Macdonald polynomials (constant term, inner product, evaluation, symmetry, Macdonald-Mehta-Cherednik), and to generalize Macdonald polynomials to the affine root system \hat A_n.

Speaker's Contact Info: etingof(at-sign)math.mit.edu