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 …

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 interpret the orthogonality relation of Kostka polynomials arising from complex reflection
groups (cf [Shoji, Invent. Math. 74 (1983), J. Algebra 245 (2001)] and [Lusztig, Adv. Math. 61 …

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 …

Let $ G $ be a real reductive Lie group with maximal compact subgroup $ K $. We
generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in …

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 …

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 …

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 …

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 introduce the local and global indices of Dirac operators for the rational Cherednik
algebra, where is a complex reflection group acting on a finite-dimensional vector space. We …