K-théorie équivariante des tours de Bott. Application à la structure multiplicative de la K-théorie équivariante des variétés de drapeaux

Abstract

(Equivariant $K$-theory of Bott towers. Application to the multiplicative structure of the equivariant $K$-theory of flag varieties)

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 in [18]