## Algebra & Number Theory

### Triple intersection formulas for isotropic Grassmannians

Vijay Ravikumar

#### 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.

#### Article information

Source
Algebra Number Theory, Volume 9, Number 3 (2015), 681-723.

Dates
Received: 25 June 2014
Revised: 7 August 2014
Accepted: 7 March 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842315

Digital Object Identifier
doi:10.2140/ant.2015.9.681

Mathematical Reviews number (MathSciNet)
MR3340548

Zentralblatt MATH identifier
1342.14109

#### Citation

Ravikumar, Vijay. Triple intersection formulas for isotropic Grassmannians. Algebra Number Theory 9 (2015), no. 3, 681--723. doi:10.2140/ant.2015.9.681. https://projecteuclid.org/euclid.ant/1510842315

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