Polynomial identities related to special Schubert varieties

A unification of permutation patterns related to Schubert varieties

We prove new connections between permutation patterns and singularities of Schubert varieties, by giving a new characterization of factorial and Gorenstein varieties in terms of so called bivincular patterns. These are generalizations of classical patterns where conditions are placed on the location of an occurrence in a permutation, as well as on the values in the occurrence. This clarifies wh...

Multiplicities on Schubert Varieties

We calculate using Macaulay 2 the multiplicities of the most singular point on Schubert varieties on Gl(n)/B for n = 5, 6. The method of computation is described and tables of the results are included.

Large Schubert Varieties

For a semisimple adjoint algebraic group G and a Borel subgroup B, consider the double classes BwB in G and their closures in the canonical compactification of G; we call these closures large Schubert varieties. We show that these varieties are normal and Cohen-Macaulay; we describe their Picard group and the spaces of sections of their line bundles. As an application, we construct geometricall...

Polynomial identities of some minimal varieties with low PI - exponent

Permutation Representations on Schubert Varieties

This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t1, t2, . . . , tn]. We show these group actions are the same as an action studied geometrically by M. Brion, and give topological meaning to the divided difference operators studied by Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and ot...