Details:
Title  Local properties of Richardson varieties in the Grassmannian via a bounded RobinsonSchenstedKnuth correspondence.  Author(s)  Victor Kreiman  Type  Article in Journal  Abstract  The Richardson variety X α γ in the Grassmannian is defined to be the intersection of the Schubert variety X γ and opposite Schubert variety X α . We give an explicit Gröbner basis for the ideal of the tangent cone at any Tfixed point of X α γ , thus generalizing a result of KodiyalamRaghavan (J. Algebra 270(1):28–54, 2003) and KreimanLakshmibai (Algebra, Arithmetic and Geometry with Applications, 2004). Our proof is based on a generalization of the RobinsonSchenstedKnuth (RSK) correspondence, which we call the bounded RSK (BRSK). We use the Gröbner basis result to deduce a formula which computes the multiplicity of X α γ at any Tfixed point by counting families of nonintersecting lattice paths, thus generalizing a result first proved by Krattenthaler (Sém. Lothar. Comb. 45:B45c, 2000/2001; J. Algebr. Comb. 22:273–288, 2005).  Keywords  Schubert variety, Grassmannian, Multiplicity  ISSN  09259899; 15729192/e 
URL 
http://link.springer.com/article/10.1007%2Fs1080100700930 
Language  English  Journal  J. Algebr. Comb.  Volume  27  Number  3  Pages  351382  Publisher  Springer US, New York, NY  Year  2008  Edition  0  Translation 
No  Refereed 
No 
