The degree of the Hilbert–Poincaré polynomial of PBW-graded modules

Backhaus, Teodor; Bossinger, Lara; Desczyk, Christian; Fourier, Ghislain

doi:10.1016/j.crma.2014.09.027

Combinatorics/Lie algebras

The degree of the Hilbert–Poincaré polynomial of PBW-graded modules
[Le degré du polynôme de Hilbert–Poincaré pour les modules PBW-gradués]

Présenté par : the Editorial Board

Backhaus, Teodor ¹ ; Bossinger, Lara ¹ ; Desczyk, Christian ¹ ; Fourier, Ghislain ^2,³

¹ Mathematisches Institut, Universität zu Köln, Germany
² Mathematisches Institut, Universität Bonn, Germany
³ School of Mathematics and Statistics, University of Glasgow, UK

Comptes Rendus. Mathématique, Tome 352 (2014) no. 12, pp. 959-963.

Résumé
Abstract

Nous étudions les polynômes de Hilbert–Poincaré pour les modules PBW-gradués associés aux modules simples d'une algèbre de Lie simple complexe. Le calcul de leur degré peut être restreint aux modules de plus haut poids fondamental. Nous donnons une formule explicite pour ces degrés.

In this note, we study the Hilbert–Poincaré polynomials for the associated PBW-graded modules of simple modules for a simple complex Lie algebra. The computation of their degree can be reduced to modules of fundamental highest weight. We provide these degrees explicitly.

Reçu le : 2014-09-04
Accepté le : 2014-09-30
Publié le : 2014-10-16

DOI : 10.1016/j.crma.2014.09.027

Affiliations des auteurs :

Backhaus, Teodor ¹ ; Bossinger, Lara ¹ ; Desczyk, Christian ¹ ; Fourier, Ghislain ^{2, 3}

¹ Mathematisches Institut, Universität zu Köln, Germany
² Mathematisches Institut, Universität Bonn, Germany
³ School of Mathematics and Statistics, University of Glasgow, UK

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     title = {The degree of the {Hilbert{\textendash}Poincar\'e} polynomial of {PBW-graded} modules},
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Backhaus, Teodor; Bossinger, Lara; Desczyk, Christian; Fourier, Ghislain. The degree of the Hilbert–Poincaré polynomial of PBW-graded modules. Comptes Rendus. Mathématique, Tome 352 (2014) no. 12, pp. 959-963. doi : 10.1016/j.crma.2014.09.027. http://www.numdam.org/articles/10.1016/j.crma.2014.09.027/

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