Le c\^one 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).