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Schubert varieties in the Grassmannian and the symplectic Grassmannian via a bounded RSK correspondence (Journal Article)

By: Contributor(s): Material type: TextTextSeries: Indian Journal of Pure and Applied Mathematics ; , Volume 54: Number 4, December 2023Publication details: New Delhi , 2023Description: 1187-1213pISSN:
  • 0019-5588
Subject(s): Online resources:
Contents:
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Summary: 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.
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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.

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