Branching problems and ${\mathfrak {sl}}(2,\mathbb {C})$-actions

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

top

Chevalley, C., Eilenberg, S., 10.1090/S0002-9947-1948-0024908-8, Trans. Amer. Math. Soc. 63 (1948), 85–124. (1948) Zbl0031.24803 MR0024908 DOI10.1090/S0002-9947-1948-0024908-8
Huang, J.-S., Pandžić, P., Dirac operators in representation theory, Mathematics: Theory and Applications, Birkhäuser Boston, 2006, pp. xii+199. (2006) Zbl1103.22008 MR2244116
Huang, J.-S., Xiao, W., 10.1007/s00029-011-0085-8, Selecta Math. (N.S.) 18 (4) (2012), 803–824. (2012) Zbl1257.22012 MR3000469 DOI10.1007/s00029-011-0085-8
Humphreys, J.E., 10.1090/gsm/094/01, Grad. Stud. Math., vol. 94, 2008. (2008) MR2428237 DOI10.1090/gsm/094/01
Kobayashi, T., Ørsted, B., Somberg, P., Souček, V., Branching laws for Verma modules and applications in parabolic geometry. II, preprint.
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) Zbl1327.53044 MR3406542
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.
Kostant, B., 10.2307/1970237, Ann. of Math. (2) 74 (2) (1961), 329–387. (1961) Zbl0134.03501 MR0142696 DOI10.2307/1970237
Kostant, B., Verma modules and the existence of quasi-invariant differential operators, Lecture Notes in Math., Springer Verlag, 1974, pp. 101–129. (1974) MR0396853
Pandžić, P., Somberg, P., Higher Dirac cohomology of modules with generalized infinitesimal character, to appear in Transform. Groups, arXiv:1310.3570.

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.