Let be a reductive Lie algebra and let be a Cartan subalgebra. A -module is called a weighted module if and only if , where each weight space is finite dimensional. The main result of the paper is the classification of all simple weight -modules. Further, we show that their characters can be deduced from characters of simple modules in category .
Soit une algèbre de Lie réductive et soit une sous-algèbre de Cartan. Un -module est dit module de poids si et seulement si il admet une décomposition , où chaque espace de poids est de dimension finie. Notre résultat principal est la classification de tous les -modules de poids simples. Également, leurs caractères sont déduits de formules des caractères des modules simples de la catégorie .
@article{AIF_2000__50_2_537_0, author = {Mathieu, Olivier}, title = {Classification of irreducible weight modules}, journal = {Annales de l'Institut Fourier}, pages = {537--592}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {50}, number = {2}, year = {2000}, doi = {10.5802/aif.1765}, zbl = {0962.17002}, mrnumber = {2001h:17017}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1765/} }
TY - JOUR AU - Mathieu, Olivier TI - Classification of irreducible weight modules JO - Annales de l'Institut Fourier PY - 2000 SP - 537 EP - 592 VL - 50 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1765/ DO - 10.5802/aif.1765 LA - en ID - AIF_2000__50_2_537_0 ER -
%0 Journal Article %A Mathieu, Olivier %T Classification of irreducible weight modules %J Annales de l'Institut Fourier %D 2000 %P 537-592 %V 50 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1765/ %R 10.5802/aif.1765 %G en %F AIF_2000__50_2_537_0
Mathieu, Olivier. Classification of irreducible weight modules. Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 537-592. doi : 10.5802/aif.1765. https://aif.centre-mersenne.org/articles/10.5802/aif.1765/
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