Details:
Title  Initial ideals of tangent cones to Schubert varieties in orthogonal Grassmannians  Author(s)  K.N. Raghavan, Shyamashree Upadhyay  Type  Article in Journal  Abstract  We compute the initial ideals, with respect to certain conveniently chosen term orders, of ideals of tangent cones at torus fixed points to Schubert varieties in orthogonal Grassmannians. The initial ideals turn out to be squarefree monomial ideals and therefore define Stanley–Reisner face rings of simplicial complexes. We describe these complexes. The maximal faces of these complexes encode certain sets of nonintersecting lattice paths.  Keywords  Orthogonal Grassmannian, Schubert variety, Initial ideal, Gröbner basis, Pfaffian, New form  ISSN  00973165 
URL 
http://www.sciencedirect.com/science/article/pii/S009731650800157X 
Language  English  Journal  Journal of Combinatorial Theory, Series A  Volume  116  Number  3  Pages  663  683  Year  2009  Edition  0  Translation 
No  Refereed 
No 
