Irreducibility of induced modules for general linear supergroups

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In this note we determine when is an induced module H⁰G(λ), corresponding to a dominant integral highest weight λof 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(λ). This extends the result of Kac who proved that, for ground fields of characteristic zero, V(λ) is irreducible if and only if λis typical.