On CherednikMacdonaldMehta identities
Authors:
Pavel Etingof and Alexander Kirillov Jr.
Journal:
Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 4347
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 MacdonaldMehta 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:
http://dx.doi.org/10.1090/S1079676298000456
PII:
S 10796762(98)000456
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
