In this paper, we study the combinatorics related to complements of tableaux. Using the representation theory of general linear groups and a known construction of the dual Weyl modules, we obtain a new straightening algorithm for bideterminants and prove that it is compatible with the complement construction of tableaux. As an application. we get a purely combinatorial construction of the isomorphisms between generalized (classical) Schur algebras introduced first by Henke, Koenig and the author. (C) 2009 Elsevier Inc. All rights reserved.
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