Formal deformations and principal series representations of SL ( 2 , ℝ ) and SL ( 2 , ℂ )

Benjamin Cahen

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 4, page 935-951
  • ISSN: 0011-4642

Abstract

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In this note, we study formal deformations of derived representations of the principal series representations of SL ( 2 , ℝ ) . In particular, we recover all the representations of the derived principal series by deforming one of them. Similar results are also obtained for SL ( 2 , ℂ ) .

How to cite

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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 70.4 (2020): 935-951. <http://eudml.org/doc/296930>.

@article{Cahen2020,
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 $\{\rm SL\}(2,\{\mathbb \{C\}\})$.},
author = {Cahen, Benjamin},
journal = {Czechoslovak Mathematical Journal},
keywords = {deformation of representation; Lie algebra; Chevalley-Eilenberg cohomology; Moyal star product; Weyl correspondence; minimal realization},
language = {eng},
number = {4},
pages = {935-951},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Formal deformations and principal series representations of $\{\rm SL\}(2,\{\mathbb \{R\}\})$ and $\{\rm SL\}(2,\{\mathbb \{C\}\})$},
url = {http://eudml.org/doc/296930},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Cahen, Benjamin
TI - Formal deformations and principal series representations of ${\rm SL}(2,{\mathbb {R}})$ and ${\rm SL}(2,{\mathbb {C}})$
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 935
EP - 951
AB - 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 ${\rm SL}(2,{\mathbb {C}})$.
LA - eng
KW - deformation of representation; Lie algebra; Chevalley-Eilenberg cohomology; Moyal star product; Weyl correspondence; minimal realization
UR - http://eudml.org/doc/296930
ER -

References

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