Czechoslovak Mathematical Journal, first online, pp. 1-17


Formal deformations and principal series representations of ${\rm SL}(2,{\mathbb R})$ and ${\rm SL}(2,{\mathbb C})$

Benjamin Cahen

Received February 3, 2019.   Published online July 1, 2020.

Abstract:  In this note, we study formal deformations of derived representations of the principal series representations of ${\rm SL}(2,{\mathbb R})$. In particular, we recover all the representations of the derived principal series by deforming one of them. Similar results are also obtained for ${\rm SL}(2,{\mathbb C})$.
Keywords:  deformation of representation; Lie algebra; Chevalley-Eilenberg cohomology; Moyal star product; Weyl correspondence; minimal realization
Classification MSC:  17B10, 17B20, 17B56, 22E46, 53D55
DOI:  10.21136/CMJ.2020.0053-19

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Affiliations:   Benjamin Cahen, Université de Lorraine, Site de Metz, UFR-MIM, Département de mathématiques, Bâtiment A, 3 rue Augustin Fresnel, BP 45112, 57073 Metz Cedex 03, France, e-mail: benjamin.cahen@univ-lorraine.fr


 
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