Schubert varieties in the Grassmannian and the symplectic Grassmannian via a bounded RSK correspondence

Papi Ray () and Shyamashree Upadhyay ()
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Papi Ray: Indian Institute of Technology, Guwahati
Shyamashree Upadhyay: Indian Institute of Technology, Guwahati

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 4, 1187-1213

Abstract: Abstract In a paper by Kodiyalam and Raghavan, they provide an explicit combinatorial description of the Hilbert function of the tangent cone at any point on a Schubert variety in the Grassmannian, by giving a certain “degree-preserving” bijection between a set of monomials defined by an initial ideal and a “standard monomial basis”. We prove here that this bijection is in fact a bounded RSK correspondence. As an application, we prove that the bijection given in a paper of Ghorpade and Raghavan (for the symplectic Grassmannian) is also a bounded RSK correspondence.

Keywords: Grassmannian; Symplectic Grassmannian; Schubert variety; Tangent cone; Hilbert function; RSK correspondence; 05E10; 14M15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00334-6

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