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

## TL;DR

This paper investigates infinite-dimensional irreducible representations of the Lie superalgebra (m|n), revealing their superdimensions relate to (m-n) dimensions and introducing new character expansion techniques.

## Contribution

It introduces a novel approach using supersymmetric Schur functions to analyze characters and superdimensions of specific (m|n) representations, providing new character expansions.

## Key findings

- Superdimension of certain representations equals the dimension of (m-n) representations.
- New character expansion formulas for supersymmetric Schur functions.
- Finite superdimensions may be relevant for supergravity models.

## 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.