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Schubert varieties in the Grassmannian and the symplectic Grassmannian via 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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Notes

  1. Proposition 2.1.2 here is the same as Proposition 4.1 of [5].

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Guwahati, Guwahati, Assam, 781039, India

    Papi Ray & Shyamashree Upadhyay

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  1. Papi Ray
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  2. Shyamashree Upadhyay
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Correspondence to Shyamashree Upadhyay.

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Communicated by Sudhir R Ghorpade.

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Ray, P., Upadhyay, S. Schubert varieties in the Grassmannian and the symplectic Grassmannian via a bounded RSK correspondence. Indian J Pure Appl Math 54, 1187–1213 (2023). https://doi.org/10.1007/s13226-022-00334-6

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  • DOI: https://doi.org/10.1007/s13226-022-00334-6

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