Double Affine Hecke Algebras and Difference Fourier Transforms

Details Double Affine Hecke Algebras and Difference Fourier Transforms Double Affine Hecke Algebras and Difference Fourier Transforms

2001-10-01

arxiv.org/abs/math/0110024v10

Mathematics

Quantum Algebra

106 pgs, LaTeX, to appear in Inventiones Math. A latex variant with some changes in Intro and Ch.7

Scientific paper

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, and various spaces of delta-functions including finite-dimensional ones, give a general description of the semisimple representations with a special consideration of the GL-case, and then gradually restrict ourselves with spherical, pseudo-unitary, and Fourier-invariant representations. The latter generalize the Verlinde algebras and lead to new Gauss-Selberg sums and Macdonald's eta-type identities.

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