On Cherednik-Macdonald-Mehta identities
Pavel Etingof, Alexander Kirillov
Abstract
In this note we give a short proof of Cherednik's generalization of Macdonald-Mehta identities for the root system An-1 using the representation theory of quantum groups. These identities, suggested and proved by Cherednik, give an explicit formula for the integral of a product of Macdonald polynomials with respect to a ``difference analogue of the Gaussian measure''.
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