Related papers: Elliptic Double Affine Hecke Algebras

We classify the elements of $W(\tilde{A}_n)$ by giving a canonical reduced expression for each, using basic tools among which affine length. We give some direct consequences for such a canonical form: a description of left multiplication by…

We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are…

The notion of trigonometric spin double affine Hecke algebras (tsDaHa) and trigonometric double affine Hecke-Clifford algebras (tDaHCa) associated to classical Weyl groups are introduced. The PBW basis property is established. An algebra…

We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are…

Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra…

For a finite central extension $\tilde{G}$ of a classical $p$-adic reductive group, we consider the endomorphism algebra of some induced projective generator \`a la Bernstein of the category of smooth representations of $\tilde{G}$. In the…

According to Kazhdan-Lusztig and Ginzburg, the Hecke algebra of an affine Weyl group is identified with the equivariant $K$-group of Steinberg's triple variety. The $K$-group is equipped with a filtration indexed by closed $G$-stable…

A systematic study of the representation theory of double affine Hecke algebras and related harmonic analysis is started in this paper. Continuing the previous papers we use the technique of intertwining operators to create Macdonald…

We introduce a new language to describe the geometry of affine Deligne-Lusztig varieties in affine flag varieties. This second part of a two paper series uses this new language, i.e. the double Bruhat graph, to describe certain structure…

In our recent papers the centralizer construction was applied to the series of classical Lie algebras to produce the quantum algebras called (twisted) Yangians. Here we extend this construction to the series of the symmetric groups S(n). We…

In this paper we give a geometric construction of Cherednik's double affine Hecke algebra. We construct the algebra as the equivariant $K$-theory of the Lagrangian subvariety of the cotangent variety of the square of the flag variety of…

The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper…

The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant…

We study a C*-dynamical system arising from the ring inclusion of the 2\times 2 integer matrices in the rational ones. The orientation preserving affine groups of these rings form a Hecke pair that is closely related to a recent…

We describe a connection between finite--dimensional representations of quantum affine algebras and affine Hecke algebras.

These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation Theory and Complex Geometry', Birkhauser 1997. Various algebras arising naturally in…

We use a degeneration of the 1D double affine Hecke algebra and the Dunkl operator to study systematically nonsymmetric Bessel functions and their truncations.

We define a concept of Hecke algebra for structure groups of set-theoretical solutions to the Yang--Baxter equation. As a comparison to Artin--Tits groups of spherical type, we study some properties of this construction, while also…

We study a class of representations over the degenerate double affine Hecke algebra of gl_n by an algebraic method. As fundamental objects in this class, we introduce certain induced modules and study some of their properties. In…

In a previous paper the author and D. Vogan defined and studied a Hecke algebra module structure on a vector space spanned by the involutions in a Weyl group. In this paper this study is continued by relating it to the asymptotic Hecke…