Jeu de taquin and diamond cone for Lie (super)algebras

In this paper, we recall combinatorial basis for shape and reduced shape algebras of the Lie algebras gl(n), sp(2n) and so(2n+1). They are given by semistandard and quasistandard tableaux. Then we generalize these constructions to the case of the Lie superalgebra spo(2n,2m+1). The main tool is an extension of Schützenberger's jeu de taquin to these algebras.