On Cherednik-Macdonald-Mehta identities

Authors:
Pavel Etingof and Alexander Kirillov Jr.

Journal:
Electron. Res. Announc. Amer. Math. Soc. **4** (1998), 43-47

MSC (1991):
Primary 05E35

Published electronically:
June 11, 1998

MathSciNet review:
1626789

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we give a proof of Cherednik's generalization of Macdonald-Mehta identities for the root system , using representation theory of quantum groups. These identities give an explicit formula for the integral of a product of Macdonald polynomials with respect to a ``difference analogue of the Gaussian measure''. They were suggested by Cherednik, who also gave a proof based on representation theory of affine Hecke algberas; our proof gives a nice interpretation for these identities in terms of representations of quantum groups and seems to be simpler than that of Cherednik.

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Additional Information

**Pavel Etingof**

Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138

Email:
etingof@math.harvard.edu

**Alexander Kirillov Jr.**

Affiliation:
Department of Mathematics, MIT, Cambridge, MA 02139

Email:
kirillov@math.mit.edu

DOI:
https://doi.org/10.1090/S1079-6762-98-00045-6

Keywords:
Macdonald polynomials

Received by editor(s):
April 14, 1998

Published electronically:
June 11, 1998

Communicated by:
David Kazhdan

Article copyright:
© Copyright 1998
American Mathematical Society