相关论文: Double affine Hecke algebras at roots of unity
In this paper, we will fully describe the representations of the crystallographic rank two affine Hecke algebras using elementary methods, for all possible values of q. The focus is on the case when q is a root of unity of small order.
We discuss q-counterparts of the Gauss integrals, a new type of Gauss-Selberg sums at roots of unity, and q-deformations of Riemann's zeta. The paper contains general results, one-dimensional formulas, and remarks about the current projects…
We use one-dimensional double affine Hecke algebras to introduce q-counterparts of the Gauss integrals and new types of Gauss-Selberg sums at roots of unity.
We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…
The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role. This result is essential for the theory of intertwiners…
We study a rational version of the double affine Hecke algebra associated to the nonreduced affine root system of type $(C^\vee_n,C_n)$. A certain representation in terms of difference-reflection operators naturally leads to the definition…
We identify the rigid dualizing complex of the (generic) affine Hecke algebra $H_q$ attached to a reduced root system and deduce some structural properties as a consequence. For example, we show that the classical Hecke algebra $H_{q^\pm}$…
Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners, and describe the…
We study star operations for Iwahori-Hecke algebras and invariant hermitian forms for finite dimensional modules over (graded) affine Hecke algebras with a view towards a unitarity algorithm.
We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine)…
We give an interpretation of the double affine Hecke algebra of Cherednik as the (suitably regularized) algebra of double cosets of a group G by a subgroup J, extending the well known interpretations of finite and affine Hecke algebras. In…
We propose a generalization of the double affine Hecke algebra of type-C C1 at specific parameters by introducing a ``Heegaard dual'' of the Hecke operators. Shown is a relationship with the skein algebra on double torus. We give…
We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extending several result and construction (presentation in terms…
The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representations are classified.
We introduce a new class (in two versions) of rational double affine Hecke algebras (DaHa) associated to the spin symmetric group. We establish the basic properties of the algebras, such as PBW and Dunkl representation, and connections to…
We describe a connection between finite--dimensional representations of quantum affine algebras and affine Hecke algebras.
For any reduced crystallographic root system, we introduce a unitary representation of the (extended) affine Hecke algebra given by discrete difference-reflection operators acting in a Hilbert space of complex functions on the weight…
Hecke algebras are usually defined algebraically, via generators and relations. We give a new algebro-geometric construction of affine and double-affine Hecke algebras (the former is known as the Iwahori-Hecke algebra, and the latter was…
We construct the basic representation of the double affine Hecke algebra at critical level $q=1$ associated to an irreducible reduced affine root system $R$ with a reduced gradient root system. For $R$ of untwisted type such a…
We give conceptual proofs of certain basic properties of the arrangement of shifted root hyperplanes associated to a root system and a Weyl group invariant real valued parameter function on the root system. The method is based on the role…