Cherednik, Ivan

From double Hecke algebra to analysis

Doc. Math. (Bielefeld) Extra Vol. ICM Berlin 1998, Vol. II, 527-537 (1998)

Summary

We discuss $q$-counterparts of the Gauss integrals, a new type of Gauss-Selberg sums at roots of unity, and $q$-deformations of Riemann's zeta-function. The paper contains general results, one-dimensional formulas, and remarks about the current projects involving the double affine Hecke algebras.

Mathematics Subject Classification

11L05, 33D80, 05A30, 11M06, 20C08, 33C80

Keywords/Phrases

double affine Hecke algebras, Fourier transform, spherical function, Macdonald polynomial, Gauss integral, Gaussian sum, metaplectic representation, Verlinde algebra, braid group, Riemann zeta-function

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