Finite dimensional representations of DAHA and affine Springers fibers : the spherical case

We classify finite dimensional simple spherical representations of rational double affine Hecke algebras, and we study a remarkable family of finite dimensional simple spherical representations of double affine Hecke algebras.Comment: 79 pages. Corrected typo

On the decomposition matrices of the quantized Schur algebra

We prove the decomposition conjecture of Leclerc and Thibon for the Schur algebra. We also give a new approach to the Lusztig conjecture for the dimension of the simple U(sl_k)-modules at roots of unity via canonical bases of the Hall algebra.Comment: AMS-tex, 30 page

On the K-theory of the cyclic quiver variety

We compute the convolution product on the equivariant K-groups of the cyclic quiver variety. We get a q-analogue of double-loop algebras, closely related to the toroidal quantum groups previously studied by the authors. We also give a geometric interpretation of the cyclic quiver variety in terms of equivariant torsion-free sheaves on the projective plane.Comment: 22 pages, AMS-te

Cyclotomic double affine Hecke algebras and affine parabolic category O, I

Using the orbifold KZ connection we construct a functor from an affine parabolic category O of type A to the category O of a cyclotomic rational double affine Hecke algebra. We give several results concerning this functor