In this review, we give an overview of several recent generalizations of the Fourier transform,
related to either the Lie algebra or the Lie superalgebra. In the former case, one obtains …

Abstract The first part (Sections 2–7) of this paper is a survey of some of the recent
developments in the theory of Dirac cohomology, especially the relationship of Dirac …

For a finite dimensional representation V of a finite reflection group W, we consider the
rational Cherednik algebra H t, c (V, W) associated with (V, W) at the parameters t≠ 0 and c …

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 …

We present recent joint work with Peter Trapa on the notion of twisted Dirac index and its
applications to (twisted) characters and to extensions of modules in a short and informal …

In this paper, we study a compact analogue of Schur-Weyl duality for real orthogonal and
symplectic groups. We analyse the functors F μ, k defined in [12], and introduce a new …

We define a family of Dirac operators for the Dunkl angular momentum algebra depending
on certain central elements of the group algebra of the Pin cover of the Weyl group inherent …

This paper is a continuation of the paper [De Bie H., Ørsted B., Somberg P., Souček V.,
Trans. Amer. Math. Soc. 364 (2012), 3875–3902], investigating a natural radial deformation …

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 …

In this paper, we study extensions of graded affine Hecke algebra modules. In particular,
based on an explicit projective resolution on graded affine Hecke algebra modules, we …