Combinatorial Aspects of An Odd Linkage Property for General Linear Supergroups

František Marko

doi:10.1007/s10468-021-10073-7

Combinatorial Aspects of An Odd Linkage Property for General Linear Supergroups

František Marko

Penn State Hazleton

Research output: Contribution to journal › Article › peer-review

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 HG0(λ), for (m|n)-hook partition λ, and properties of certain morphisms ψ_k to derive results related to odd linkage for G over a field F of characteristic different from 2.

Original language	English (US)
Pages (from-to)	1429-1460
Number of pages	32
Journal	Algebras and Representation Theory
Volume	25
Issue number	6
DOIs	https://doi.org/10.1007/s10468-021-10073-7
State	Published - Dec 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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abstract = "Let G = GL(m|n) be a general linear supergroup, and Gev be its even subsupergroup isomorphic to GL(m) ×GL(n). In this paper, we use the explicit description of Gev-primitive vectors in the costandard supermodule ∇(λ), the largest polynomial G-subsupermodule of the induced supermodule HG0(λ), for (m|n)-hook partition λ, and properties of certain morphisms ψk to derive results related to odd linkage for G over a field F of characteristic different from 2.",

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AB - Let G = GL(m|n) be a general linear supergroup, and Gev be its even subsupergroup isomorphic to GL(m) ×GL(n). In this paper, we use the explicit description of Gev-primitive vectors in the costandard supermodule ∇(λ), the largest polynomial G-subsupermodule of the induced supermodule HG0(λ), for (m|n)-hook partition λ, and properties of certain morphisms ψk to derive results related to odd linkage for G over a field F of characteristic different from 2.

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Combinatorial Aspects of An Odd Linkage Property for General Linear Supergroups

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