Abstract

In the Grothendieck cohomology of a flag variety G/H there are two canonical additive bases, namely, the Demazure basis [M. Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. Éc. Norm. Sup. (4) 7 (1974), 53–88.] and the Grothendieck basis [B. Kostant and S. Kumar, T-equivariant K-theory of generalized flag varieties, J. Diff. Geom. 32 (1990), no. 2, 549–603.].

We present explicit formulae that reduce the multiplication of these basis elements to the Cartan numbers of G.