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On Cherednik-Macdonald-Mehta identities

Pavel Etingof·Alexander Kirillov Jr
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Abstract

In this note we give a short proof of Cherednik's generalization of Macdonald-Mehta identities for the root system $A_{n-1}$ 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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Pavel Etingof, Alexander Kirillov Jr. 1997-12-23. On Cherednik-Macdonald-Mehta identities. https://arxiv.org/abs/q-alg/9712051

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