Some properties of general linear supergroups and of Schur superalgebras. (Russian, English) Zbl 1118.16029
Algebra Logika 45, No. 3, 257-299 (2006); translation in Algebra Logic 45, No. 3, 147-171 (2006).
Summary: It is shown that the category of rational supermodules over a general linear supergroup is a highest weight category. More exactly, we construct superanalogs of the theory of modules with good filtration and of the dual theory of modules with Weyl’s. Using these, we show that indecomposable injective supermodules have good filtration of a certain kind.
MSC:
| 16W55 | “Super” (or “skew”) structure |
| 17A70 | Superalgebras |
| 20G05 | Representation theory for linear algebraic groups |
| 20C30 | Representations of finite symmetric groups |
Keywords:
indecomposable injective supermodules; general linear supergroups; Schur superalgebras; highest weight categories; modules with good filtrations; modules with Weyl filtrationsReferences:
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