Irreducibility of induced modules for general linear supergroups

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.