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In a paper by Ghorpade and Raghavan, they provide an explicit combinatorialdescription of the Hilbert function of the tangent cone at any point on aSchubert variety in the symplectic Grassmannian, by giving a certain"degree-preserving" bijection between a set of monomials defined by an initialideal and a "standard monomial basis". We prove here that this bijection is infact a bounded RSK correspondence.

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