We produce a new basis for the Schur and Weyl modules associated to a
row-convex shape, D. The basis is indexed by 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.Comment: 31 pages, latex2e, submitted to J. Algebr