Combinatorial aspects of the linkage principle for general linear supergroups

2016/09/06 by František Marko, Frantisek Marko, Marko, Frantisek
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1609.01783

openalex publication_date 2016/09/06 · openalex created_date 2016/09/16 · arxiv created 2020/11/05 · arxiv updated 2020/11/06 · openalex updated_date 2026/07/28

Abstract

Let G=GL(m|n) be a general linear supergroup and G_ev be its even subsupergroup isomorphic to GL(m)× GL(n). In this paper we use the explicit description of G_ev-primitive vectors in the costandard supermodule ∇(λ), the largest polynomial G-subsupermodule of the induced supermodule H⁰_G(λ), for (m|n)-hook partition λ, and a properties of certain morphisms ψ_k to derive results related to the odd linkage for G over a field F of characteristic different from 2.

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• Blocks for general linear supergroup GL(m|n)
• Even-primitive vectors in induced supermodules for general linear supergroups and in costandard supermodules for Schur superalgebras
• A combinatorial approach to Donkin-Koppinen filtrations of general linear supergroups
• Linkage for periplectic supergroups in positive characteristic