Dunkl operators. (English) Zbl 0916.33012

Heckman, G. J.

Séminaire Bourbaki. Volume 1996/97. Exposés 820–834. Paris: Société Mathématique de France, Astérisque. 245, 223-246, Exp. No. 828 (1997).

This is a survey paper on the trigonometric Dunkl operators and it concerns the following items: basic properties of the Dunkl operators, connection between Dunkl operators and the hypergeometric theory for root systems, the Knizhnik-Zamolodchikov connection, relations with hypergeometric shift operators, etc.
For the entire collection see [Zbl 0910.00034].

Reviewer: E.Minchev (Sofia)

MSC:

33C80	Connections of hypergeometric functions with groups and algebras, and related topics
22E70	Applications of Lie groups to the sciences; explicit representations
33C70	Other hypergeometric functions and integrals in several variables
33C67	Hypergeometric functions associated with root systems
33D67	Basic hypergeometric functions associated with root systems
39A70	Difference operators

Keywords:

Dunkl operators