7 citations · 11 across the 2 of their papers we have counts for
9 papers · 1 filter
Introduction to double Hecke algebras
Ivan Cherednik
This paper is based on the introduction to the monograph ``Double affine Hecke algebras'' to be published by Cambridge University Press. The connections with Knizhnik-Zamolodchikov…
Diagonal Coinvariants and Double Affine Hecke Algebras
Ivan Cherednik
We establish a q-generalization of Gordon's theorem that the space of diagonal coinvariants has a quotient identified with a perfect representation of the rational double affine He…
From Double Hecke algebra to Fourier transform
Ivan Cherednik, Viktor Ostrik
The paper contains a systematic theory of the one-dimensional Double Hecke algebra, including applications to the difference Fourier transform, Macdonald's polynomials, Gaussian su…
Double Affine Hecke Algebras and Difference Fourier Transforms
Ivan Cherednik
In the paper, we introduce and calculate difference Fourier transforms on representations of the double affine Hecke algebras in polynomilas, polynomials multiplied by the Gaussian…
Hankel transform via double Hecke algebra
Ivan Cherednik, Yavor Markov
We use a degeneration of the 1D double affine Hecke algebra and the Dunkl operator to study systematically nonsymmetric Bessel functions and their truncations.
One-dimensional double Hecke algebras and Gaussians
Ivan Cherednik
We use one-dimensional double affine Hecke algebras to introduce q-counterparts of the Gauss integrals and new types of Gauss-Selberg sums at roots of unity.