We define an analogue of the Casimir element for a graded affine Hecke algebra H, and
then introduce an approximate square-root called the Dirac element. Using it, we define the …

We define uniformly the notions of Dirac operators and Dirac cohomology in the framework
of the Hecke algebras introduced by Drinfeld (Anal i Prilozhen 20 (1): 69–70, 1986). We …

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 …

We define the algebraic Dirac induction map is a Hecke algebra analog of the explicit
realization of the Baum–Connes assembly map in the-algebra of a real reductive group …

In this paper, we give a uniform construction of irreducible genuine characters of the Pin
cover W˜ of a Weyl group W, and put them into the context of theory of Springer …

This paper presents a natural generalisation of Saxl conjecture from a Lie-theoretical
perspective, which is verified for the exceptional types. For classical types, progress is made …

I present several applications of the Dirac inequality to the determination of isolated unitary
representations and associated “spectral gaps” in the case of unramified principal series …

We introduce a notion of elliptic fake degrees for unipotent elliptic representations of a
semisimple-adic group. We conjecture, and verify in some cases, that the relation between …

We give a new and independent parametrization of the set of discrete series characters of
an affine Hecke algebra ℋ v, in terms of a canonically defined basis ℬ gm of a certain lattice …

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