Initial Ideals of Tangent Cones to the Richardson Varieties in the Orthogonal Grassmannian

Abstract EN

A Richardson variety Xαγ in the Orthogonal Grassmannian is defined to be the intersection of a Schubert variety Xγ in the Orthogonal Grassmannian and an opposite Schubert variety Xα therein.

We give an explicit description of the initial ideal (with respect to certain conveniently chosen term order) for the ideal of the tangent cone at any T-fixed point of Xαγ, thus generalizing a result of Raghavan and Upadhyay (2009).

Our proof is based on a generalization of the Robinson-Schensted-Knuth (RSK) correspondence, which we call the Orthogonal-bounded-RSK (OBRSK).