A bideterminant basis for a reductive monoid

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JournalJournal of Pure and Applied Algebra
DatePublished - May 2012
Issue number5
Volume216
Number of pages15
Pages (from-to)1207-1221
Original languageEnglish

Abstract

We use the rational tableaux introduced by Stembridge to give a bideterminant basis for a normal reductive monoid and for its variety of noninvertible elements. We also obtain a bideterminant basis for the full coordinate ring of the general linear group and for all its truncations with respect to saturated sets. Finally, we deduce an alternative proof of the double centraliser theorem for the rational Schur algebra and the walled Brauer algebra over an arbitrary infinite base field which was first obtained by Dipper, Doty and Stoll. (C) 2011 Elsevier B.V. All rights reserved.

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