Dunkl operators. (English) Zbl 0916.33012

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)


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


Dunkl operators
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