The gamma filtrations of K-theory of complete flag varieties

TL;DR

This paper computes the gamma filtration of the complex K-theory of complete flag varieties G/T, using the Chow ring of the versal flag variety, providing new insights into their algebraic structure.

Contribution

It introduces a method to compute the gamma filtration of K-theory for complete flag varieties using Chow rings, which was not previously established.

Findings

Explicit description of gr_{gamma}(G/T) for complete flag varieties

Connection established between K-theory gamma filtration and Chow ring

New computational techniques for algebraic K-theory of flag varieties

Abstract

Let G be a simply connected compact Lie group and T its maximal torus. We compute the graded ring gr_{gamma}(G/T) associated with the gamma filtration of the complex K-theory K(G/T). We use the Chow ring of the corresponding versal flag variety.