| Title:
|
Branching problems and ${\mathfrak{sl}}(2,\mathbb{C})$-actions (English) |
| Author:
|
Pandžić, Pavle |
| Author:
|
Somberg, Petr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
51 |
| Issue:
|
5 |
| Year:
|
2015 |
| Pages:
|
331-346 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
representation theory of simple Lie algebra |
| Keyword:
|
generalized Verma modules |
| Keyword:
|
singular vectors and composition series |
| Keyword:
|
relative Lie algebra and Dirac cohomology |
| MSC:
|
22E47 |
| idZBL:
|
Zbl 06537734 |
| idMR:
|
MR3449112 |
| DOI:
|
10.5817/AM2015-5-331 |
| . |
| Date available:
|
2016-01-11T10:12:28Z |
| Last updated:
|
2017-02-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144774 |
| . |
| Reference:
|
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| Reference:
|
[2] Huang, J.-S., Pandžić, P.: Dirac operators in representation theory.Mathematics: Theory and Applications, Birkhäuser Boston, 2006, pp. xii+199. Zbl 1103.22008, MR 2244116 |
| Reference:
|
[3] Huang, J.-S., Xiao, W.: Dirac cohomology of highest weight modules.Selecta Math. (N.S.) 18 (4) (2012), 803–824. Zbl 1257.22012, MR 3000469, 10.1007/s00029-011-0085-8 |
| Reference:
|
[4] Humphreys, J.E.: Representations of Semisimple Lie Algebras in the BGG Category ${mathcal O}$.Grad. Stud. Math., vol. 94, 2008. MR 2428237, 10.1090/gsm/094/01 |
| Reference:
|
[5] Kobayashi, T., Ørsted, B., Somberg, P., Souček, V.: Branching laws for Verma modules and applications in parabolic geometry. II.preprint. |
| Reference:
|
[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. Zbl 1327.53044, MR 3406542 |
| Reference:
|
[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. |
| Reference:
|
[8] Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem.Ann. of Math. (2) 74 (2) (1961), 329–387. Zbl 0134.03501, MR 0142696, 10.2307/1970237 |
| Reference:
|
[9] Kostant, B.: Verma modules and the existence of quasi-invariant differential operators.Lecture Notes in Math., Springer Verlag, 1974, pp. 101–129. MR 0396853 |
| Reference:
|
[10] Pandžić, P., Somberg, P.: Higher Dirac cohomology of modules with generalized infinitesimal character.to appear in Transform. Groups, arXiv:1310.3570. |
| . |
