Vol. 9, No. 3, 2015

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Triple intersection formulas for isotropic Grassmannians

Vijay Ravikumar

Vol. 9 (2015), No. 3, 681–723

Let X be an isotropic Grassmannian of type B, C, or D. In this paper we calculate K-theoretic Pieri-type triple intersection numbers for X: that is, the sheaf Euler characteristic of the triple intersection of two arbitrary Schubert varieties and a special Schubert variety in general position. We do this by determining explicit equations for the projected Richardson variety corresponding to the two arbitrary Schubert varieties, and show that it is a complete intersection in projective space. The K-theoretic Pieri coefficients are alternating sums of these triple intersection numbers, and we hope they will lead to positive Pieri formulas for isotropic Grassmannians.

triple intersection numbers, isotropic Grassmannian, orthogonal Grassmannian, submaximal Grassmannian, Richardson variety, projected Richardson variety, Pieri rule, $K$-theoretic Pieri formula, $K$-theoretic triple intersection
Mathematical Subject Classification 2010
Primary: 14N15
Secondary: 19E08, 14M15
Received: 25 June 2014
Revised: 7 August 2014
Accepted: 7 March 2015
Published: 17 April 2015
Vijay Ravikumar
Mathematics Department
Chennai Mathematical Institute
Kelambakkam 603103