Central elements in the distribution algebra of a general linear supergroup and supersymmetric elements

František Marko, Alexandr N. Zubkov

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1 Citation (Scopus)

Abstract

In this paper we investigate the image of the center Z of the distribution algebra Dist(GL(m|n)) of the general linear supergroup over a ground field of positive characteristic under the Harish-Chandra morphism h:Z→Dist(T) obtained by the restriction of the natural map Dist(GL(m|n))→Dist(T). We define supersymmetric elements in Dist(T) and show that each image h(c) for c∈Z is supersymmetric. The central part of the paper is devoted to a description of a minimal set of generators of the algebra of supersymmetric elements over Frobenius kernels Tr.

Original languageEnglish
Pages (from-to)89-118
Number of pages30
JournalJournal of Algebra
Volume553
DOIs
Publication statusPublished - Jul 1 2020

Keywords

  • Center of the distribution algebra of a torus
  • Supersymmetric elements

ASJC Scopus subject areas

  • Algebra and Number Theory

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