Algebra & Number Theory

Triple intersection formulas for isotropic Grassmannians

Vijay Ravikumar

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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

Subjects
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]

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

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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