Irreducibility of induced supermodules for general linear supergroups

In this note we determine when an induced supermodule H-G(0)(lambda), corresponding to a dominant integral highest weight lambda of the general linear supergroup G = GL(m vertical bar n), is irreducible. Using the contravariant duality given by the supertrace we obtain a characterization of irreducibility of Weyl supermodules V(lambda). This extends the result of Kac ([12], [13]) who proved that, for ground fields of characteristic zero, V(lambda) is irreducible if and only if lambda is typical. (C) 2017 Elsevier Inc. All rights reserved.