Branching problems and 𝔰𝔩 ( 2 , ℂ ) -actions

Pavle Pandžić; Petr Somberg

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 5, page 331-346
  • ISSN: 0044-8753

Abstract

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We study certain 𝔰𝔩 ( 2 , ℂ ) -actions associated to specific examples of branching of scalar generalized Verma modules for compatible pairs ( 𝔤 , 𝔭 ) , ( 𝔤 ' , 𝔭 ' ) of Lie algebras and their parabolic subalgebras.

How to cite

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Pandžić, Pavle, and Somberg, Petr. "Branching problems and ${\mathfrak {sl}}(2,\mathbb {C})$-actions." Archivum Mathematicum 051.5 (2015): 331-346. <http://eudml.org/doc/276064>.

@article{Pandžić2015,
abstract = {We study certain $\{\mathfrak \{sl\}\}(2,\mathbb \{C\})$-actions associated to specific examples of branching of scalar generalized Verma modules for compatible pairs $(\mathfrak \{g\},\mathfrak \{p\})$, $(\mathfrak \{g\}^\{\prime \},\mathfrak \{p\}^\{\prime \})$ of Lie algebras and their parabolic subalgebras.},
author = {Pandžić, Pavle, Somberg, Petr},
journal = {Archivum Mathematicum},
keywords = {representation theory of simple Lie algebra; generalized Verma modules; singular vectors and composition series; relative Lie algebra and Dirac cohomology; representation theory of simple Lie algebra; generalized Verma modules; singular vectors and composition series; relative Lie algebra and Dirac cohomology},
language = {eng},
number = {5},
pages = {331-346},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Branching problems and $\{\mathfrak \{sl\}\}(2,\mathbb \{C\})$-actions},
url = {http://eudml.org/doc/276064},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Pandžić, Pavle
AU - Somberg, Petr
TI - Branching problems and ${\mathfrak {sl}}(2,\mathbb {C})$-actions
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 5
SP - 331
EP - 346
AB - We study certain ${\mathfrak {sl}}(2,\mathbb {C})$-actions associated to specific examples of branching of scalar generalized Verma modules for compatible pairs $(\mathfrak {g},\mathfrak {p})$, $(\mathfrak {g}^{\prime },\mathfrak {p}^{\prime })$ of Lie algebras and their parabolic subalgebras.
LA - eng
KW - representation theory of simple Lie algebra; generalized Verma modules; singular vectors and composition series; relative Lie algebra and Dirac cohomology; representation theory of simple Lie algebra; generalized Verma modules; singular vectors and composition series; relative Lie algebra and Dirac cohomology
UR - http://eudml.org/doc/276064
ER -

References

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  1. Chevalley, C., Eilenberg, S., 10.1090/S0002-9947-1948-0024908-8, Trans. Amer. Math. Soc. 63 (1948), 85–124. (1948) Zbl0031.24803MR0024908DOI10.1090/S0002-9947-1948-0024908-8
  2. Huang, J.-S., Pandžić, P., Dirac operators in representation theory, Mathematics: Theory and Applications, Birkhäuser Boston, 2006, pp. xii+199. (2006) Zbl1103.22008MR2244116
  3. Huang, J.-S., Xiao, W., 10.1007/s00029-011-0085-8, Selecta Math. (N.S.) 18 (4) (2012), 803–824. (2012) Zbl1257.22012MR3000469DOI10.1007/s00029-011-0085-8
  4. Humphreys, J.E., 10.1090/gsm/094/01, Grad. Stud. Math., vol. 94, 2008. (2008) MR2428237DOI10.1090/gsm/094/01
  5. Kobayashi, T., Ørsted, B., Somberg, P., Souček, V., Branching laws for Verma modules and applications in parabolic geometry. II, preprint. 
  6. Kobayashi, T., Ørsted, B., Somberg, P., Souček, V., Branching laws for Verma modules and applications in parabolic geometry. I, Adv. Math. 285 (2015), 1–57. (2015) Zbl1327.53044MR3406542
  7. Kobayashi, T., Pevzner, M., Differential symmetry breaking operators. I-General theory and F-method. II-Rankin-Cohen operators for symmetric pairs, to appear in Selecta Math., arXiv:1301.2111. 
  8. Kostant, B., 10.2307/1970237, Ann. of Math. (2) 74 (2) (1961), 329–387. (1961) Zbl0134.03501MR0142696DOI10.2307/1970237
  9. Kostant, B., Verma modules and the existence of quasi-invariant differential operators, Lecture Notes in Math., Springer Verlag, 1974, pp. 101–129. (1974) MR0396853
  10. Pandžić, P., Somberg, P., Higher Dirac cohomology of modules with generalized infinitesimal character, to appear in Transform. Groups, arXiv:1310.3570. 

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