Geodesic
Formal deformations and principal series representations of ${\rm SL}(2,{\mathbb R})$ and ${\rm SL}(2,{\mathbb C})$
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 935-951.

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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 ${\rm SL}(2,{\mathbb C})$.
DOI : 10.21136/CMJ.2020.0053-19
Classification : 17B10, 17B20, 17B56, 22E46, 53D55
Keywords: deformation of representation; Lie algebra; Chevalley-Eilenberg cohomology; Moyal star product; Weyl correspondence; minimal realization 
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Cahen, Benjamin. Formal deformations and principal series representations of ${\rm SL}(2,{\mathbb R})$ and ${\rm SL}(2,{\mathbb C})$. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 935-951. doi : 10.21136/CMJ.2020.0053-19. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0053-19/

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