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 K⁰(G/T) for G = Spin(n). In particular, we give a counterexample for a conjecture by Karpenko when G = Spin(17).