Cells and constructible representations in type .
Character polynomials, their -analogs and the Kronecker product.
Constant term identities, orthogonal polynomials and affine Hecke algebras.
Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
We define the -restriction and -induction functors on the category of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.