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Description of costandard modules for Schur superalgebra $S (2 | 2)$ in positive characteristic

A. N. Grishkov

Instituto de Mathemática e Estatística, Universidade de São Paulo, Rua do Matão 1010 CEP 05508-090, São Paulo, Brazil

Omsk State University n.a. F.M. Dostoevskii, pr. Mira 55-A, Omsk 644077, Russia

E-mail Address: shuragri@gmail.com

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and

F. Marko

Penn State Hazleton, 76 University Drive, Hazleton PA 18202, USA

E-mail Address: fxm13@psu.edu

Corresponding author.

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https://doi.org/10.1142/S021949881850038XCited by:1 (Source: Crossref)

Abstract

In this paper, we shall describe costandard modules $\nabla (λ)$ of restricted highest weight $λ$ for Schur superalgebra $S (2 | 2)$ over an algebraically closed field $K$ of positive characteristic $p > 2$ . Additionally, for a restricted highest weight $λ$ , we determine all composition factors of the costandard module $\nabla (λ)$ ; in particular we compute the decomposition numbers in the process of the modular reduction of a simple module with a restricted highest weight.

Communicated by E. Zelmanov

Keywords:

AMSC: 17A70, 20G05, 15A72, 13A50, 05E15

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