Table of Contents
International Journal of Combinatorics
Volume 2013 (2013), Article ID 392437, 19 pages
http://dx.doi.org/10.1155/2013/392437
Research Article

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

School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India

Received 26 October 2012; Accepted 9 January 2013

Academic Editor: Nantel Bergeron

Copyright © 2013 Shyamashree Upadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Richardson variety in the Orthogonal Grassmannian is defined to be the intersection of a Schubert variety in the Orthogonal Grassmannian and an opposite Schubert variety 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 , 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).