Algebra/Lie algebras
Generalized Joseph's decompositions
Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 887-892.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.07.002
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, Volume 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/

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Cited by 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.).