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arXiv · 1904.00074

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

N. I. Stoilova·J. Thierry-Mieg·J. Van der Jeugt
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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 $[0,\ldots,0,p]$. We have shown that the superdimension of $[0,\ldots,0,p]$ 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.

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N. I. Stoilova, J. Thierry-Mieg, J. Van der Jeugt. 2019-03-29. On characters and superdimensions of some infinite-dimensional irreducible representations of $\mathfrak{osp}(m|n)$. https://doi.org/10.1134/s1063778818060285

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