Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Grassmannian

TL;DR

This paper provides explicit positive formulas for restricting Schubert classes to fixed points in the equivariant K-theory and cohomology of Grassmannians, utilizing Grobner degenerations of Schubert varieties.

Contribution

It introduces new positive formulas for Schubert class restrictions in equivariant theories, based on Grobner degeneration techniques near fixed points.

Findings

Formulas are positive and explicit for Schubert class restrictions.

Uses Grobner degeneration results from prior work to derive formulas.

Applicable to both equivariant K-theory and cohomology of Grassmannians.

Abstract

We give positive formulas for the restriction of a Schubert Class to a T-fixed point in the equivariant K-theory and equivariant cohomology of the Grassmannian. Our formulas rely on a result of Kodiyalam-Raghavan and Kreiman-Lakshmibai, which gives an equivariant Grobner degeneration of a Schubert variety in the neighborhood of a T-fixed point of the Grassmannian.