Abstract.
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.
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*""Partially supported by NSF grants DMS-0200276.
**""Partially supported by NSF grants DMS-0098830.
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Cherednik, I., Ostrik, V. From double Hecke algebra to Fourier transform. Sel. math., New ser. 9, 161–249 (2003). https://doi.org/10.1007/s00029-003-0329-3
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DOI: https://doi.org/10.1007/s00029-003-0329-3