This is a survey paper about affine Hecke algebras. We start from scratch and discuss some
algebraic aspects of their representation theory, referring to the literature for proofs. We aim …

Let $\mathcal R $ be a root datum with affine Weyl group $ W $, and let $\mathcal
H=\mathcal H (\mathcal R, q) $ be an affine Hecke algebra with positive, possibly unequal …

We introduce graded Hecke algebras ℍ\mathbb H based on a (possibly disconnected)
complex reductive group G and a cuspidal local system ℒ\mathcal L on a unipotent orbit of a …

We establish a transfer of unitarity for a Bernstein component of the category of smooth
representations of a reductive $ p $-adic group to the associated Hecke algebra, in the …

For a Weyl group W, we investigate simple closed formulas (valid on elliptic conjugacy
classes) for the character of the representation of W in the homology of a Springer fiber. We …

Let H be a graded Hecke algebra with complex deformation parameters and Weyl group W.
We show that the Hochschild, cyclic and periodic cyclic homologies of H are all independent …

We present a geometric description for tempered modules of the affine Hecke algebra of
type Cn with arbitrary (non-root of unity) unequal parameters, using the exotic Deligne …

The Iwahori--Matsumoto involution $\mathsf {IM} $ is an algebra involution on an affine
Hecke algebra. To a connected complex reductive group $ G $, Lusztig associated various …

Let H be an affine Hecke algebra in the sense of Lusztig (see [16] or [25]). The Fréchet
algebra S, the Schwartz algebra completion of H, is a central object of study for the harmonic …

Spin representations of Weyl groups and the Springer correspondence Page 1 J. reine angew.
Math. 671 (2012), 199—222 DOI 10.1515/CRELLE.2011.160 Journal für die reine und …