Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

In this note we give a proof of Cherednik's generalization of Mac\-donald--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.

Copyright 1998 American Mathematical Society

TeX source (31K)
DVI (34K)
PostScript (134K)

Article Info

• ERA Amer. Math. Soc. 04 (1998), pp. 43-47
• Publisher Identifier: S 1079-6762(98)00045-6
• 1991 Mathematics Subject Classification. Primary 5E35
• Key words and phrases. Macdonald polynomials
• Received by the editors April 14, 1998
• Posted on June 11, 1998
• Communicated by David Kazhdan
• Comments (When Available)

Pavel Etingof

Department of Mathematics, Harvard University, Cambridge, MA 02138

E-mail address: etingof@math.harvard.edu

Alexander Kirillov, Jr.

Department of Mathematics, MIT, Cambridge, MA 02139

E-mail address: kirillov@math.mit.edu