## 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.

Original language | English |
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Pages (from-to) | 147-166 |

Number of pages | 20 |

Journal | Journal of Algebra and its Applications |

Volume | 7 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 |

Externally published | Yes |

## Keywords

- Costandard module
- Schur superalgebra
- Tableaux

## ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics