Good filtrations for generalized Schur algebras

TL;DR

This paper proves that tensor products of standard modules over generalized Schur superalgebras have standard filtrations, extending the theory of good filtrations in the context of quasi-hereditary superalgebras.

Contribution

It establishes that tensor products of standard modules over generalized Schur bi-superalgebras admit standard filtrations, advancing the understanding of module structures in superalgebra theory.

Findings

Tensor products of standard modules have standard filtrations.

Generalized Schur bi-superalgebras are quasi-hereditary.

Extension of good filtration theory to superalgebra context.

Abstract

Given a quasi-hereditary superalgebra $A$, the first author and R. Muth have defined generalized Schur bi-superalgebras $T^A(n)$ and proved that these algebras are again quasi-hereditary. In particular, $T^A(n)$ comes with a family of standard modules. Developing the work of Donkin and Mathieu on good filtrations, we prove that tensor product of standard modules over $T^A(n)$ has a standard filtration.