Symmetric Spaces and star representations III. The Poincare Disk

2002/09/17 by Pierre Bieliavsky, P. Bieliavsky, Bieliavsky, P. +2
Mathematics · #22E46 #53C35 #81S10 #FOS: Mathematics #Mathematics and Applications #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:22E46 #msc:53C35 #msc:81S10

paper · pdf · doi:10.48550/arxiv.math/0209206

arxiv created 2002/09/17 · openalex publication_date 2002/09/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article is a contribution to the domain of (convergent) deformation quantization of symmetric spaces by use of Lie groups representation theory. We realize the regular representation of SL(2,\R) on the space of smooth functions on the Poincaré disc as a sub-representation of SL(2,\R) in the Weyl-Moyal star product algebra on \R². We indicate how it is possible to extend our construction to the general case of a Hermitian symmetric space of tube type.

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