A Uniform Proof of the Macdonald-Mehta-Opdam Identity for Finite Coxeter Groups
Name
Etingof MRL 2010.pdf
Size
117.11 KB
Format
Adobe PDF
Checksum (MD5)
c261876d056a6ff9c1e60474f09bf1a1
Author(s)
Etingof, Pavel I.
Date Issued
March 2010
Journal
Mathematical Research Letters
Publisher
International Press
Citation
Etingof, Pavel. "A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups." Mathematical Research Letters, 17 (2010), no.2, 275–282
Version
Author's final manuscript
Abstract
In this note we give a new proof of the Macdonald-Mehta-Opdam integral identity for finite Coxeter groups (in the equal parameter case). This identity was conjectured by Macdonald and proved by Opdam in \cite{O1,O2} using the theory of multivariable Bessel functions, but in non-crystallographic cases the proof relied on a computer calculation by F. Garvan. Our proof is somewhat more elementary (in particular, it does not use multivariable Bessel functions), and uniform (does not refer to the classification of finite Coxeter groups). \footnote{We expect that this proof can be generalized to the case of non-equal parameters. Indeed, many of the steps of our proof, including key Proposition \ref{l2}, generalize without effort to this setting.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
http://www.mrlonline.org/mrl/2010-017-002/2010-017-002-007.html
