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 λ m = 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.

Costandard modules over Schur superalgebras in characteristic $p$

LA SCALA, Roberto;
2008

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 λ m = 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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/15158
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 11
social impact