TL;DR
This paper generalizes rational Schur algebras to the super setting, establishing a Schur-Weyl duality and conditions for semisimplicity, thereby advancing the understanding of rational supermodules of the general linear supergroup.
Contribution
It introduces rational Schur superalgebras, extending classical theory to superalgebras and establishing duality results and semisimplicity conditions.
Findings
Established Schur-Weyl duality for rational Schur superalgebras
Proved semisimplicity under certain conditions
Provided a new approach to studying rational supermodules
Abstract
We develop and study the generalization of rational Schur algebras to the super setting. Similar to the classical case, this provides a new method for studying rational supermodules of the general linear supergroup . Furthermore, we establish a Schur-Weyl duality result for rational Schur superalgebras and conclude that under certain conditions these objects will be semisimple.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry