Local Properties of Richardson Varieties in the Grassmannian via a Bounded Robinson-Schensted-Knuth Correspondence
Abstract
Description
We give an explicit Grobner basis for the ideal of the tangent cone at any T-fixed point of a Richardson variety in the Grassmannian, thus generalizing a result of Kodiyalam-Raghavan and Kreiman-Lakshmibai. Our proof is based on a generalization of the Robinson-Schensted-Knuth (RSK) correspondence, which we call the bounded RSK (BRSK). We use the Grobner basis result to deduce a formula which computes the multiplicity of the Richardson variety at any T-fixed point by counting families of nonintersecting lattice paths, thus generalizing a result first proved by Krattehthaler.
34 pages, final version, many revisions, to appear in Journal of Algebraic Combinatorics
34 pages, final version, many revisions, to appear in Journal of Algebraic Combinatorics