On Characters and Superdimensions of Some Infinite-Dimensional Irreducible Representations of osp(m|n)

Abstract

Chiral spinors and self dual tensors of the Lie superalgebra osp(m|n) are infinite-dimensional representations belonging to the class of representations with Dynkin labels [0,..., 0, p]. We show that the superdimension of [0,..., 0, p] coincides with the dimension of a so(m − n) representation. When the superdimension is finite, these representations could play a role in supergravity models. Our technique is based on expansions of characters in terms of supersymmetric Schur functions. In the process of studying these representations, we obtain new character expansions.