On Cherednik-Macdonald-Mehta identities

Details On Cherednik-Macdonald-Mehta identities On Cherednik-Macdonald-Mehta identities

1997-12-23

arxiv.org/abs/q-alg/9712051v1

Mathematics

Quantum Algebra

7 pages, amstex

Scientific paper

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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