Affine cellularity of affine Hecke algebras of rank two

Representations of rank two affine Hecke algebras

This paper classifies and constructs explicitly all the irreducible representations of affine Hecke algebras of rank two root systems. The methods used to obtain this classification are primarily combinatorial and are, for the most part, an application of the methods used in [Ra1]. I have made special effort to describe how the classification here relates to the classifications by Langlands par...

Generalized Double Affine Hecke Algebras of Higher Rank

Hecke group algebras as degenerate affine Hecke algebras

The Hecke group algebra H W̊ of a finite Coxeter group W̊ , as introduced by the first and last author, is obtained from W̊ by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when W̊ is the classical Weyl group associated to an affine Weyl group W . Namely, we prove that, for q not a root of unity, H W̊ is the ...

Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory

We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r, p, n) and the corresponding cyclotomic Hecke algebras Hr,p,n, can be obtained, in all cases, from the affine Hecke algebra of type A. The Young tableaux theory was extended to affine Hec...

Analytic R-groups of Affine Hecke Algebras

Date: September 7, 2009. 2000 Mathematics Subject Classification. Primary 20C08; Secondary 22D25, 22E35, 43A30. During the preparation of this paper the first named author was supported by the program ANR-08-BLAN-01. During the preparation of this paper the second named author was partially supported by a Pionier grant of the Netherlands Organization for Scientific Research (NWO). He also enjoy...