Double affine Hecke algebras, conformal coinvariants and Kostka polynomials

We study a class of representations called 'calibrated representations' of the rational and trigonometric double affine Hecke algebras of type GL_n. We give a realization of calibrated irreducible modules as spaces of coinvariants constructed from integrable modules over the affine Lie algebra over(gl, ̂)_m. We also give a character formula of these irreducible modules in terms of a generalization of Kostka polynomials. These results are conjectured by Arakawa, Suzuki and Tsuchiya based on the conformal field theory. The proofs using recent results on the representation theory of the double affine Hecke algebras will be presented in the forthcoming papers. To cite this article: T. Suzuki, C. R. Acad. Sci. Paris, Ser. I 343 (2006).