GOOD FILTRATIONS FOR GENERALIZED SCHUR ALGEBRAS

Given a quasi-hereditary superalgebra A, the first author and R. Muth have defined generalized Schur bi-superalgebras TA(n) and proved that these algebras are again quasi-hereditary. In particular, TA(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 TA(n) has a standard filtration.