Let W be the wreath product of a symmetric group with a cyclic group of order l. The corresponding restricted rational Cherednik algebra is a finite dimensional algebra whose block structure has a combinatorial description in terms of J-hearts. We show that this description is equivalent to one given in terms of residues of multipartitions. This establishes links with Rouquier families for the ...

We introduce an algebra H consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type (C ∨ 1 , C1). We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra H, and the corresponding Fourier transforms. These eigenfunctions are non-symmetric v...

We begin the study of unitary representations of Hecke algebras of complex reflections groups. We obtain a complete classification for the Hecke algebra of the symmetric group Sn over the complex numbers. Interestingly, the unitary representations in the category O for the rational Cherednik algebra of type A studied in [ESG] correspond to the unitary representations of the corresponding Hecke ...

The goal of this paper is to define a new class of objects which we call triple groups and to relate them with Cherednik’s double affine Hecke algebras. This has as immediate consequences new descriptions of double affine Weyl and Artin groups, the double affine Hecke algebras as well as the corresponding elliptic objects. From the new descriptions we recover results of Cherednik on automorphis...

Let A be a maximal (or more generally a hereditary) order in a central simple algebra over a global field F of positive characteristic. We show that certain modular scheme of A-elliptic sheaves– for different A – are twists of each other and deduce that the uniformization at ∞ and the Cherednik-Drinfeld uniformization for these varieties are equivalent. 2010 Mathematics Subject Classification: ...