A Straightening Algorithm for Row-Convex Tableaux

Abstract We produce a new basis for the Schur and Weyl modules associated to a row-convex shape D. The basis is indexed by a new class of “straight” tableaux which we introduce by weakening the usual requirements for standard tableaux. Spanning is proved via a new straightening algorithm for expanding elements of the representation into this basis. For skew shapes, this algorithm specializes to the classical straightening law. The new straight basis is used to produce bases for flagged Schur and Weyl modules, to provide Groebner and SAGBI bases for the homogeneous coordinate rings of some configuration varieties, and to produce a flagged branching rule for row-convex representations. Systematic use of supersymmetric letterplace techniques enables the representation theoretic results to be applied to representations of the general linear Lie superalgebra as well as to the general linear group.