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ISSN 1079-6762

 

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: In this note we give a proof of Cherednik's generalization of Macdonald-Mehta identities for the root system $A_{n-1}$, 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: http://dx.doi.org/10.1090/S1079-6762-98-00045-6
PII: S 1079-6762(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