Nous généralisons la décomposition de introduite par A. Joseph [5] et la relions, pour 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 , 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 introduced by A. Joseph in [5] and link it, for 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 whose elements behave as Schur polynomials and thus explicitly identify the center with the ring of symmetric functions.
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@article{CRMATH_2015__353_10_887_0, author = {Berenstein, Arkady and Greenstein, Jacob}, title = {Generalized {Joseph's} decompositions}, journal = {Comptes Rendus. Math\'ematique}, pages = {887--892}, publisher = {Elsevier}, volume = {353}, number = {10}, year = {2015}, doi = {10.1016/j.crma.2015.07.002}, language = {en}, url = {http://www.numdam.org./articles/10.1016/j.crma.2015.07.002/} }
TY - JOUR AU - Berenstein, Arkady AU - Greenstein, Jacob TI - Generalized Joseph's decompositions JO - Comptes Rendus. Mathématique PY - 2015 SP - 887 EP - 892 VL - 353 IS - 10 PB - Elsevier UR - http://www.numdam.org./articles/10.1016/j.crma.2015.07.002/ DO - 10.1016/j.crma.2015.07.002 LA - en ID - CRMATH_2015__353_10_887_0 ER -
%0 Journal Article %A Berenstein, Arkady %A Greenstein, Jacob %T Generalized Joseph's decompositions %J Comptes Rendus. Mathématique %D 2015 %P 887-892 %V 353 %N 10 %I Elsevier %U http://www.numdam.org./articles/10.1016/j.crma.2015.07.002/ %R 10.1016/j.crma.2015.07.002 %G en %F CRMATH_2015__353_10_887_0
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/
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☆ The authors are partially supported by the NSF grant DMS-1403527 (A. B.) and by the Simons Foundation collaboration grant no. 245735 (J. G.).