On Schur algebras and related algebras VI: some remarks on rational and classical Schur algebras

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Abstract

In a recent paper, Dipper and Doty, [2], 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, [16], 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.
Original languageEnglish
Number of pages31
JournalJournal of Algebra
Publication statusAccepted/In press - 2013

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