Local properties of Schubert Varieties in the Symplectic Grassmannian via a bounded RSK correspondence

TL;DR

This paper reveals that a combinatorial bijection describing the Hilbert function of tangent cones in symplectic Grassmannian Schubert varieties is actually a bounded RSK correspondence, linking algebraic geometry with combinatorics.

Contribution

It establishes that the explicit bijection used in previous work is a bounded RSK correspondence, providing a new combinatorial perspective.

Findings

The bijection is a bounded RSK correspondence.

Connects algebraic geometry of Schubert varieties with combinatorial algorithms.

Enhances understanding of tangent cone properties in symplectic Grassmannians.

Abstract

In a paper by Ghorpade 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 symplectic 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.