2009/09/08 by Shyamashree Upadhyay, Upadhyay, Shyamashree
Mathematics · #05E10 (Primary) 14N15 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:05E10 #msc:14N15
paper · pdf · doi:10.48550/arxiv.0909.1424
42 Pages, 3 figures
arxiv created 2009/09/08 · openalex publication_date 2009/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Richardson variety X_\ga^\gc in the Orthogonal Grassmannian is defined to be the intersection of a Schubert variety X^\gc in the Orthogonal Grassmannian and a opposite Schubert variety X_\ga therein. We give an explicit description of the initial ideal (with respect to certain conveniently chosen term order) for the ideal of the tangent cone at any T-fixed point of X_\ga^\gc, thus generalizing a result of Raghavan-Upadhyay \citeRa-Up2. Our proof is based on a generalization of the Robinson-Schensted-Knuth (RSK) correspondence, which we call the Orthogonal bounded RSK (OBRSK). The OBRSK correspondence will give a degree-preserving bijection between a set of monomials defined by the initial ideal of the ideal of the tangent cone (as mentioned above) and a `standard monomial basis'. A similar work for Richardson varieties in the ordinary Grassmannian was done by Kreiman in \citeKr-bkrs.