Le cône diamant symplectique

Abstract : The diamond cone is a combinatorial description for a basis in a indecomposable module for the nilpotent factor n+ of a semi simple Lie algebra. After N.J. Wildberger who introduced this notion for sl(3), this description was achevied by N. Bel Baraka, N.J. Wildberger and D. A. for sl(n) and by B. Agrebaoui and ourselves for the rank 2 semi-simple Lie algebras. In the present work, we generalize these constructions to the Lie algebras sp(2n). The symplectic semi-standard Young tableaux were defined by C. de Concini, they form a basis for the shape algebra of sp(2n). We introduce here the notion of symplectic quasi-standard Young tableaux, these tableaux describe the diamond cone for sp(2n).
Document type :
Journal articles
Complete list of metadatas

Cited literature [8 references]  Display  Hide  Download

Contributor : Didier Arnal <>
Submitted on : Tuesday, July 14, 2009 - 10:10:52 AM
Last modification on : Sunday, June 2, 2019 - 5:48:02 PM
Long-term archiving on : Tuesday, June 15, 2010 - 8:00:11 PM


Files produced by the author(s)


  • HAL Id : hal-00403918, version 1
  • ARXIV : 0907.2450



Didier Arnal, Olfa Khlifi. Le cône diamant symplectique. Bulletin des Sciences Mathématiques, Elsevier, 2010, 134 (6), pp.635-663. ⟨hal-00403918⟩



Record views


Files downloads