#### Vol. 9, No. 3, 2015

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Triple intersection formulas for isotropic Grassmannians

### Vijay Ravikumar

Vol. 9 (2015), No. 3, 681–723
##### Abstract

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.

##### Keywords
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