Comptes Rendus
no. 10
Algebra/Lie algebras
Generalized Joseph's decompositions
[Décompositions de Joseph généralisées]

Présenté par : the Editorial Board

Arkady Berenstein1 ; Jacob Greenstein2
1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
2 Department of Mathematics, University of California Riverside, Riverside, CA 92521, USA
Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 887-892.

Nous généralisons la décomposition de Uq(g) introduite par A. Joseph [5] et la relions, pour g semi-simple, au calcul bien connu d'éléments centraux dû à V. Drinfeld [2]. Dans ce cas, nous construisons une base naturelle dans le centre de Uq(g), dont les éléments se conduisent comme des polynômes de Schur, et nous identifions donc explicitement le centre avec l'anneau de fonctions symétriques.

We generalize the decomposition of Uq(g) introduced by A. Joseph in [5] and link it, for g semisimple, to the celebrated computation of central elements due to V. Drinfeld [2]. In that case, we construct a natural basis in the center of Uq(g) whose elements behave as Schur polynomials and thus explicitly identify the center with the ring of symmetric functions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.07.002
Arkady Berenstein 1 ; Jacob Greenstein 2

1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
2 Department of Mathematics, University of California Riverside, Riverside, CA 92521, USA 
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Arkady Berenstein; Jacob Greenstein. Generalized Joseph's decompositions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 887-892. doi : 10.1016/j.crma.2015.07.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.07.002/

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Cité par Sources :

☆ The authors are partially supported by the NSF grant DMS-1403527 (A. B.) and by the Simons Foundation collaboration grant no. 245735 (J. G.).

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