Description of Costandard Modules of Schur Superalgebra S(3 ☐1)

Let S(m {pipe} n) be a Schur superalgebra over a base field K of any characteristic different from 2. The characters of simple S(m {pipe} n)-modules and composition factors of costandard modules ∇(λ) for restricted weights λ were determined for the Schur superalgebra S(2 {pipe} 1) in [6] and for Schur superalgebra S(2 {pipe} 2) in [4] and [5]. The goal of this article is to obtain corresponding results for Schur superalgebra S(3 {pipe} 1). Additionally, we determine the character of ∇(λ) for all Schur superalgebras S(m {pipe} 1), where m ≥ 1.