Resumen de From double Hecke algebra to Fourier transform

Ivan Cherednik, Viktor Ostrik

• The paper contains a systematic theory of the one-dimensional double affine Hecke algebra including applications to the difference Fourier transform, the Rogers-Macdonald polynomials, the Gaussian sums at roots of unity, and the Verlinde algebras. The main new result is the classification of finite dimensional representations for generic q and at the roots of unity.