Diamond module for the Lie algebra so(2n+1,C)
Abstract
The diamond cone is a combinatorial description for a basis of an indecomposable module for the nilpotent factor
n
of a semi simple Lie algebra. After N. J. Wildberger who introduced this notion, this description was achevied for
sl(n)
, the rank 2 semi-simple Lie algebras and
sp(2n)
. In the present work, we generalize these constructions to the Lie algebras
so(2n+1)
. The orthogonal semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they form a basis for the shape algebra of
so(2n+1)
. Defining the notion of orthogonal quasistandard Young tableaux, we prove these tableaux give a basis for the diamond module for
so(2n+1)
.