2001/11/30 by Ivan Cherednik, Viktor Ostrik
Mathematics · #math.QA #math.RT
published as Sel. math., New Ser. 9 (2003), 161-249 · Sections 8,9 are updated
arxiv created 2004/04/11 · arxiv updated 2009/11/30
The paper contains a systematic theory of the one-dimensional Double Hecke algebra, including applications to the difference Fourier transform, Macdonald's polynomials, Gaussian sums at roots of unity, and Verlinde algebras. The main result is the classification of finite-dimensional representations for generic q and at roots of unity.