Irreducibility of induced supermodules for general linear supergroups

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

Original languageEnglish (US)
Pages (from-to)92-110
Number of pages19
JournalJournal of Algebra
StatePublished - Jan 15 2018

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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