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

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.

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Accepté le :
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DOI : 10.1016/j.crma.2014.09.027
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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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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