Macdonald polynomials and quantum gl(n)
refreshments at 3:45pm
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
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