Irreducibility of induced modules for general linear supergroups

TL;DR

This paper characterizes when induced modules for the general linear supergroup are irreducible, extending Kac's characteristic zero result to a broader context using supertrace duality.

Contribution

It provides a new criterion for irreducibility of induced modules and Weyl modules for GL(m|n), generalizing Kac's characteristic zero findings.

Findings

Characterization of irreducibility of induced modules H^0_G()

Extension of Kac's irreducibility criterion to broader contexts

Use of supertrace duality for module analysis

Abstract

In this note we determine when is an induced module H^0_G(\lambda), corresponding to a dominant integral highest weight \lambda of the general linear supergroup G=GL(m|n) irreducible. Using the contravariant duality given by the supertrace we obtain a characterization of irreducibility of Weyl modules V(\lambda). This extends the result of Kac who proved that, for ground fields of characteristic zero, V(\lambda) is irreducible if and only if \lambda is typical.