A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups

Details A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups

2009-03-29

arxiv.org/abs/0903.5084v1

Mathematics

Representation Theory

10 pages, latex

Scientific paper

We give a new proof of the Macdonald-Mehta-Opdam integral identity for finite Coxeter groups. This identity was conjectured by Macdonald and proved by Opdam in 1993 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 and does not use computers).

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