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hal-00095163, version 1

On Fock spaces and SL(2)-triples for Dunkl operators

Salem Ben Said () 1, Bent Orsted 2

(2005) accepté pour publication

Abstract: In this paper we begin with the construction of a generalized Segal-Bargmann transform related to every root system with finite reflection group $G.$ To do so, we introduce a Hilbert space $\cal F_k(\C^N)$ of holomorphic functions with reproducing kernel equal to the Dunkl kernel. Moreover, by means of an $\s\l(2)$-triple, we prove the branching decomposition of $\cal F_k(\C^N)$ as a unitary $G\times \widetilde{SL(2,\R)}$-module. Further applications of the $\s\l(2)$-triple to the Dunkl theory are given. This paper is a survey of recent results in [BO3] and [BO4], and it also contains new results.

• 1:  Institut Elie Cartan Nancy (IECN)
• CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
• 2:  Aarhus University
• Aarhus University
• Domain : Mathematics/Functional Analysis

• hal-00095163, version 1
• oai:hal.archives-ouvertes.fr:hal-00095163
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• Submitted on: Friday, 15 September 2006 12:44:43
• Updated on: Friday, 15 September 2006 13:03:57