The gamma filtrations for the spin groups. (English) Zbl 1478.22005
Summary: Let \(G\) be a compact Lie group and \(T\) its maximal torus. In this paper, we try to compute \(gr_{\gamma}^*(G/T)\) the graded ring associated with the gamma filtration of the complex \(K\)-theory \(K^0(G/T)\) for \(G=\operatorname{Spin}(n)\). In particular, we give a counterexample for a conjecture by Karpenko when \(G=\operatorname{Spin}(17)\).
MSC:
| 22E10 | General properties and structure of complex Lie groups |
| 14C15 | (Equivariant) Chow groups and rings; motives |
| 19D99 | Higher algebraic \(K\)-theory |
| 20G15 | Linear algebraic groups over arbitrary fields |
| 57T15 | Homology and cohomology of homogeneous spaces of Lie groups |
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