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

Abstract

Chiral spinors and self dual tensors of the Lie superalgebra $\mathfrak{osp}(m|n)$ 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 $\mathfrak{so}(m-n)$ 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.

arXiv admin note: text overlap with arXiv:1609.06350, arXiv:1904.00067

References in corpus (2)

• The parafermion Fock space and explicit so(2n+1) representations
• A class of infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n) and the parastatistics Fock space