Representations for Lie superalgebras of type C

Abstract

Let G =osp(2,2n) be the classical Lie superalgebra of type C of rank n +1. Let λ be a partition with λ 1 ⩽ n . Then λ labels a finite-dimensional irreducible G -module, V ( λ ). We describe the character of V ( λ ) in terms of tableaux. This tableaux description of characters enable us to decompose T =⊗ f V , the f -fold tensor product of the natural representation of G , into its irreducible submodules and to show that the centralizer algebra of G on T is isomorphic to the Brauer algebra B f (2−2 n ) for n > f .