Hochschild homology of affine Hecke algebras

Details Hochschild homology of affine Hecke algebras Hochschild homology of affine Hecke algebras

2011-08-26

arxiv.org/abs/1108.5286v1

Mathematics

K-Theory and Homology

37 pages

Scientific paper

Let H = H (R,q) be an affine Hecke algebra with complex, possibly unequal parameters q, which are not roots of unity. We compute the Hochschild and the cyclic homology of H. It turns that these are independent of q and that they admit an easy description in terms of the extended quotient of a torus by a Weyl group, both of which are canonically associated to the root datum R. For q positive we also prove that the representations of the family of algebras H (R,q^e) come in families which depend analytically on the complex number e. Analogous results are obtained for graded Hecke algebras and for Schwartz completions of affine Hecke algebras.

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