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

X iv : m at h . Q A / 0 50 40 89 v 4 1 2 Ju n 20 06 GENERALIZED DOUBLE AFFINE HECKE ALGEBRAS OF HIGHER RANK

Iwahori-hecke Algebras of Sl2 over 2-dimensional Local Fields

Hecke algebras were first studied because of their role in the representation theory of p-adic groups, or algebraic groups over 1-dimensional local fields. There are two important classes of Hecke algebras. One is spherical Hecke algebras attached to maximal compact open subgroups, and the other is Iwahori-Hecke algebras attached to Iwahori subgroups. A spherical Hecke algebra is isomorphic to ...

1 N ov 2 00 1 INVOLUTIONS OF DOUBLE AFFINE HECKE ALGEBRAS

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 of double affine Hecke algebras.