Abstract
Let be an affine Hecke algebra with a positive parameter function . We are interested in the topological K-theory of its -completion . We prove that does not depend on the parameter , solving a long-standing conjecture of Higson and Plymen. For this we use representation-theoretic methods, in particular elliptic representations of Weyl groups and Hecke algebras.
Thus, for the computation of these K-groups it suffices to work out the case . These algebras are considerably simpler than for , just crossed products of commutative algebras with finite Weyl groups. We explicitly determine for all classical root data . This will be useful for analyzing the K-theory of the reduced -algebra of any classical -adic group.
For the computations in the case , we study the more general situation of a finite group acting on a smooth manifold . We develop a method to calculate the K-theory of the crossed product . In contrast to the equivariant Chern character of Baum and Connes, our method can also detect torsion elements in these K-groups.
Citation
Maarten Solleveld. "Topological K-theory of affine Hecke algebras." Ann. K-Theory 3 (3) 395 - 460, 2018. https://doi.org/10.2140/akt.2018.3.395
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