Factorial Schur and Grothendieck polynomials from Bott Samelson varieties

TL;DR

This paper demonstrates that factorial Schur and Grothendieck polynomials serve as representatives for Schubert classes in equivariant cohomology and K-theory, using Bott-Samelson resolutions and localization techniques.

Contribution

It establishes a geometric interpretation of factorial Schur and Grothendieck polynomials via Bott-Samelson resolutions of Schubert varieties.

Findings

Factorial Schur functions represent Schubert classes in equivariant cohomology.

Factorial Grothendieck polynomials represent Schubert classes in equivariant K-theory.

Uses Bott-Samelson resolutions and localization techniques for proofs.

Abstract

We use Bott-Samelson resolutions of Schubert varieties in Grassmannians along with equiariant localization techniques to show that the factorial Schur functions and the factorial Grothendieck polynomials represent Schubert classes in equivariant cohomology and equivariant K-theory respectively.