On characters and superdimensions of some infinite-dimensional irreducible representations of $\mathfrak{o}\mathfrak{s}\mathfrak{p}(m\mathrm{\mid }n)$

Chiral spinors and self dual tensors of the Lie superalgebra $\mathfrak{o}\mathfrak{s}\mathfrak{p}(m\mathrm{\mid }n)$ are infinite dimensional representations belonging to the class of representations with Dynkin labels $[0,\dots ,0,p]$. We have shown that the superdimension of $[0,\dots ,0,p]$ coincides with the dimension of a $\mathfrak{s}\mathfrak{o}(m-n)$ 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.