I will describe a new class of "metaplectic" representations of the double affine Hecke algebra, which generalize the usual polynomial representation. This gives rise to a new family of "metaplectic" polynomials, which generalize Macdonald polynomials.
Our construction is motivated by the theory of Weyl group multiple Dirichlet series, and the work of Kazhdan-Patterson (for type GL_n) and Chinta-Gunnells (for arbitrary root systems).
This is joint work with J. Stokman and V. Venkateswaran