Generalized double affine Hecke algebras of higher rank

Generalized Double Affine Hecke Algebras of Higher Rank

A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank

We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for Uq(slN ). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld–Kohno theorem for Knizhnik–Zamolodchikov differential equations, we prove that the explicit representatio...

A pr 2 00 5 GENERALIZED DOUBLE AFFINE HECKE ALGEBRAS OF HIGHER RANK

Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces

Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G= Z Z2, where is 2, 3, 4, and 6, r...

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...