Restriction to Levi subalgebras and generalization of the category 𝒪

Guillaume Tomasini[1]

  • [1] Institut de Recherche Mathématique Avancée Université de Strasbourg 7 rue René Descartes 67084 Strasbourg

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 1, page 37-88
  • ISSN: 0373-0956

Abstract

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The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple.

How to cite

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Tomasini, Guillaume. "Restriction to Levi subalgebras and generalization of the category $\mathcal{O}$." Annales de l’institut Fourier 63.1 (2013): 37-88. <http://eudml.org/doc/275672>.

@article{Tomasini2013,
abstract = {The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple.},
affiliation = {Institut de Recherche Mathématique Avancée Université de Strasbourg 7 rue René Descartes 67084 Strasbourg},
author = {Tomasini, Guillaume},
journal = {Annales de l’institut Fourier},
keywords = {weight modules; cuspidal modules; branching rules},
language = {eng},
number = {1},
pages = {37-88},
publisher = {Association des Annales de l’institut Fourier},
title = {Restriction to Levi subalgebras and generalization of the category $\mathcal\{O\}$},
url = {http://eudml.org/doc/275672},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Tomasini, Guillaume
TI - Restriction to Levi subalgebras and generalization of the category $\mathcal{O}$
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 1
SP - 37
EP - 88
AB - The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple.
LA - eng
KW - weight modules; cuspidal modules; branching rules
UR - http://eudml.org/doc/275672
ER -

References

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