# On superdimensions of some infinite-dimensional irreducible representations of $osp(m|n)$

## TL;DR

This paper explores the superdimension of certain infinite-dimensional representations of the Lie superalgebra $osp(m|n)$, revealing a correspondence with $so(m-n)$ representations and extending this to more complex cases.

## Contribution

It extends the known superdimension correspondence from simpler to more complex $osp(2m|2n)$ representations with additional Dynkin labels.

## Key findings

- Superdimension of $osp(m|n)$ representations matches $so(m-n)$ dimensions.
- Extension of the $osp(m|n) o so(m-n)$ correspondence to more complex representations.
- Provides formulas and insights relevant for supergravity theories.

## Abstract

In a recent paper characters and superdimension formulas were investigated for the class of representations with Dynkin labels $[0,\ldots,0,p]$ of the Lie superalgebra $osp(m|n)$. Such representations are infinite-dimensional, and of relevance in supergravity theories provided their superdimension is finite. We have shown that the superdimension of such representations coincides with the dimension of a $so(m-n)$ representation. In the present contribution, we investigate how this $osp(m|n)\sim so(m-n)$ correspondence can be extended to the class of $osp(2m|2n)$ representations with Dynkin labels $[0,\ldots,0,q,p]$.