Algebra & Number Theory
- Algebra Number Theory
- Volume 9, Number 3 (2015), 681-723.
Triple intersection formulas for isotropic Grassmannians
Let be an isotropic Grassmannian of type , , or . In this paper we calculate -theoretic Pieri-type triple intersection numbers for : 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 -theoretic Pieri coefficients are alternating sums of these triple intersection numbers, and we hope they will lead to positive Pieri formulas for isotropic Grassmannians.
Algebra Number Theory, Volume 9, Number 3 (2015), 681-723.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14N15: Classical problems, Schubert calculus
Secondary: 19E08: $K$-theory of schemes [See also 14C35] 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
triple intersection numbers isotropic Grassmannian orthogonal Grassmannian submaximal Grassmannian Richardson variety projected Richardson variety Pieri rule $K$-theoretic Pieri formula $K$-theoretic triple intersection
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