In a recent paper, Dipper and Doty, , introduced certain finite dimensional algebras, associated with the natural module of the general linear group and its dual, which they call rational Schur algebras. We give a proof, via tilting modules, that these algebra are in fact generalized Schur algebras. Using the same technique we show that certain finite dimensional algebras with classical groups, introduced by Doty, , are quasi hereditary algebras. A generalized Schur algebras may be viewed as a quotient of the algebra of distributions of a reductive group by a certain ideal. We give generators for this ideal.
|Number of pages||31|
|Journal||Journal of Algebra|
|Publication status||Accepted/In press - 2013|