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

2005/11/29 by Victor Kreiman, V. Kreiman, Kreiman, V. · 1 citation
Mathematics · #05E10 #14M15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #math.CO #msc:05E10 #msc:14M15

paper · pdf · doi:10.48550/arxiv.math/0511695

34 pages, final version, many revisions, to appear in Journal of Algebraic Combinatorics

openalex publication_date 2005/11/29 · arxiv created 2008/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Multiplicity at any torus-fixed point in a Richardson variety in the Symplectic Grassmannian

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