Classification of irreducible weight modules

Olivier Mathieu

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 2, page 537-592
  • ISSN: 0373-0956

Abstract

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Let 𝔤 be a reductive Lie algebra and let 𝔥 be a Cartan subalgebra. A 𝔤 -module M is called a weighted module if and only if M = ⊕ λ M λ , where each weight space M λ is finite dimensional. The main result of the paper is the classification of all simple weight 𝔤 -modules. Further, we show that their characters can be deduced from characters of simple modules in category 𝒪 .

How to cite

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Mathieu, Olivier. "Classification of irreducible weight modules." Annales de l'institut Fourier 50.2 (2000): 537-592. <http://eudml.org/doc/75429>.

@article{Mathieu2000,
abstract = {Let $\{\frak g\}$ be a reductive Lie algebra and let $\{\frak h\}$ be a Cartan subalgebra. A $\{\frak g\}$-module $M$ is called a weighted module if and only if $M =\oplus _\lambda M_\lambda $, where each weight space $M_\lambda $ is finite dimensional. The main result of the paper is the classification of all simple weight $\{\frak g\}$-modules. Further, we show that their characters can be deduced from characters of simple modules in category $\{\cal O\}$.},
author = {Mathieu, Olivier},
journal = {Annales de l'institut Fourier},
keywords = {semisimple Lie algebras; weight modules; reductive algebra; simple weight modules; cuspidal modules; Lie algebras of type and ; coherent families},
language = {eng},
number = {2},
pages = {537-592},
publisher = {Association des Annales de l'Institut Fourier},
title = {Classification of irreducible weight modules},
url = {http://eudml.org/doc/75429},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Mathieu, Olivier
TI - Classification of irreducible weight modules
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 2
SP - 537
EP - 592
AB - Let ${\frak g}$ be a reductive Lie algebra and let ${\frak h}$ be a Cartan subalgebra. A ${\frak g}$-module $M$ is called a weighted module if and only if $M =\oplus _\lambda M_\lambda $, where each weight space $M_\lambda $ is finite dimensional. The main result of the paper is the classification of all simple weight ${\frak g}$-modules. Further, we show that their characters can be deduced from characters of simple modules in category ${\cal O}$.
LA - eng
KW - semisimple Lie algebras; weight modules; reductive algebra; simple weight modules; cuspidal modules; Lie algebras of type and ; coherent families
UR - http://eudml.org/doc/75429
ER -

References

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