Row-convex tableaux and the combinatorics of initial terms

Straightening Laws for Row-Convex Tableaux

We introduce the notion of a straight tableau and prove that the straight tableaux of xed row-convex shape form a basis for the GL n -representations and the general linear Lie superalgebra representations associated to the given shape. We provide a straightening algorithm for expressing arbitrary tableaux in terms of straight tableaux. These techniques can be modi ed to provide bases for repre...

A Straighteng Algorithm for Row-convex Tableaux. 0

Nullcone for the Symplectic Group and Related Combinatorics

We study the nullcone for the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.

Kronecker Products, Characters, Partitions, and the Tensor Square Conjectures

We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups Sn contain all irreducibles as their constituents. Our main result is that they contain representations corresponding to hooks and two row Young diagrams. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of c...

A straightening algorithm for row-convex tableaux

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 classi...