Generalized Joseph's decompositions

Berenstein, Arkady; Greenstein, Jacob

doi:10.1016/j.crma.2015.07.002

Algebra/Lie algebras

Generalized Joseph's decompositions
[Décompositions de Joseph généralisées]

Présenté par : the Editorial Board

Berenstein, Arkady ¹ ; Greenstein, Jacob ²

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, Tome 353 (2015) no. 10, pp. 887-892.

Résumé
Abstract

Nous généralisons la décomposition de $U_{q} (g)$ 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 $U_{q} (g)$ , 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 $U_{q} (g)$ 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 $U_{q} (g)$ whose elements behave as Schur polynomials and thus explicitly identify the center with the ring of symmetric functions.

Reçu le : 2015-04-23
Accepté le : 2015-07-09
Publié le : 2015-08-06

DOI : 10.1016/j.crma.2015.07.002

Affiliations des auteurs :

Berenstein, Arkady ¹ ; Greenstein, Jacob 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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Berenstein, Arkady; Greenstein, Jacob. Generalized Joseph's decompositions. Comptes Rendus. Mathématique, Tome 353 (2015) no. 10, pp. 887-892. doi : 10.1016/j.crma.2015.07.002. http://www.numdam.org/articles/10.1016/j.crma.2015.07.002/

Bibliographie
Cité par

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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.).