The Gamma filtrations for the Spin groups

Abstract

Let G be a compact Lie group and T its maximal torus. In this paper, we try to compute gr * γ (G/T ) the graded ring associated with the gamma filtration of the complex K-theory K 0 (G/T ) for G = Spin(n). In particular, we show gr * γ (G/T ) is not isomorphic to CH * (G/B) when G = Spin(17) and G is a versal G-torsor.