From Double Hecke algebra to Fourier transform

Mathematics – Quantum Algebra

Scientific paper

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Scientific paper

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.

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