Costandard modules over schur superalgebras in characteristic p

Roberto La Scala, Alexander Zubkov

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

In this paper we consider the problem of describing the costandard modules ∇ (λ) of a Schur superalgebra S(m n,r) over a base field K of arbitrary characteristic. Precisely, if G = GL (m n) is a general linear supergroup and Dist (G) its distribution superalgebra we compute the images of the Kostant ℤ-form under the epimorphism Dist (G) → S(m n,r). Then, we describe ∇(λ) as the null-space of some set of superderivations and we obtain an isomorphism ∇(λ) ≈ ∇(λ+ 0)⊗∇ (0 λ-) assuming that λ = (λ+ λ-) and λm = 0. If char (K) = p we give a Frobenius isomorphism ∇(0 pμ) ≈ ∇(μ)p where ∇(μ) is a costandard module of the ordinary Schur algebra S(n,r). Finally we provide a characteristic free linear basis for ∇(λ 0) which is parametrized by a set of superstandard tableaux.

Original languageEnglish
Pages (from-to)147-166
Number of pages20
JournalJournal of Algebra and its Applications
Volume7
Issue number2
DOIs
Publication statusPublished - 2008
Externally publishedYes

Keywords

  • Costandard module
  • Schur superalgebra
  • Tableaux

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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