Journal article

A pieri-chevalley formula in the K-theory of a G/B-bundle

H Pittie, A Ram

Electronic Research Archive | Published : 1999

Abstract

Let G be a semisimple complex Lie group, B a Borel subgroup, and T ⊆ B a maximal torus of G. The projective variety G/B is a generalization of the classical flag variety. The structure sheaves of the Schubert subvarieties form a basis of the K-theory K(G/B) and every character of T gives rise to a line bundle on G/B. This note gives a formula for the product of a dominant line bundle and a Schubert class in K(G/B). This result generalizes a formula of Chevalley which computes an analogous product in cohomology. The new formula applies to the relative case, the K-theory of a G/B-bundle over a smooth base X, and is presented in this generality. In this setting the new formula is a generalizati..

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