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Chiral spinors and self dual tensors of the Lie superalgebra$\mathfrak{osp}(m|n)$ are infinite dimensional representations belonging to theclass of representations with Dynkin labels $[0,\ldots,0,p]$. We have shownthat the superdimension of $[0,\ldots,0,p]$ coincides with the dimension of a$\mathfrak{so}(m-n)$ representation. When the superdimension is finite, theserepresentations could play a role in supergravity models. Our technique isbased on expansions of characters in terms of supersymmetric Schur functions.In the process of studying these representations, we obtain new characterexpansions.

On characters and superdimensions of some infinite-dimensional irreducible representations of $\mathfrak{osp}(m|n)$