Irreducibility of induced modules for general linear supergroups

2013/09/02 by František Marko, Frantisek Marko, Marko, Frantisek · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1309.0284

arxiv created 2013/09/02 · openalex publication_date 2013/09/02 · arxiv updated 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we determine when is an induced module H⁰_G(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.

Cited by

• GL(m|n)-supermodules with good and Weyl filtrations

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