K-theorie equivariante des varietes de Bott-Samelson. Application a la structure multiplicative de la K-theorie equivariante des varietes de drapeaux

TL;DR

This paper constructs a basis for the equivariant K-theory of Bott towers and Bott-Samelson varieties, providing explicit descriptions of their multiplicative structures and a method to compute structure constants for flag varieties.

Contribution

It introduces a new basis for the equivariant K-theory of Bott towers and Bott-Samelson varieties, enabling explicit calculations of their multiplicative structures.

Findings

Constructed a basis for the equivariant K-theory of Bott towers.

Described the multiplicative structure of these K-theories.

Provided a method to compute structure constants for flag varieties.

Abstract

We construct a basis of the equivariant $K$-theory of Bott towers, and we describe precisely the multiplicative structure of these algebras. We deduce similar results for Bott-Samelson varieties. Thanks to the link between flag varieties and Bott-Samelson varieties, we give a method to compute the structure constants of the equivariant $K$-theory of flag varieties in the basis constructed by Kostant and Kumar.