Canonical bilinear form and Euler characters

TL;DR

This paper provides an explicit formula for the canonical bilinear form on the Grothendieck ring of the Lie supergroup GL(n,m) and introduces an algorithm for decomposing Euler characters into irreducible module characters.

Contribution

It presents a new explicit formula for the canonical bilinear form and an algorithm for decomposing Euler characters in the context of Lie supergroups.

Findings

Explicit formula for the canonical bilinear form on Grothendieck ring

Algorithm for decomposing Euler characters into irreducible modules

Application to partially polynomial representations

Abstract

An explicit formula for the canonical bilinear form on the Grothendieck ring of the Lie supergroup $GL(n,m)$ is given. As an application we get an algorithm for the decomposition Euler characters in terms of characters of irreducible modules in the category of partially polynomial representations.