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Local Properties of Richardson Varieties in the Grassmannian via a Bounded Robinson-Schensted-Knuth Correspondence

V. Kreiman
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Abstract

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.

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V. Kreiman. 2008-03-04. Local Properties of Richardson Varieties in the Grassmannian via a Bounded Robinson-Schensted-Knuth Correspondence. https://arxiv.org/abs/math/0511695

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