Double affine Hecke algebras and difference Fourier transforms

By I. Cherednik. 2001

59 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c2910fb5c5b671d84652ed17215c92006417c791

How researchers see this paper

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In Geometry and Topology

1. V. Ginzburg
2. Pavel Etingof
3. I. Gordon
4. Y. Berest
5. I. Losev
6. R. Bezrukavnikov
7. J. T. Stafford
8. Stephen Griffeth

In Mathematical Physics

1. Pavel Etingof
2. V. Ginzburg
3. I. Gordon
4. Y. Berest
5. I. Losev
6. R. Bezrukavnikov
7. J. T. Stafford
8. A. Premet

In Statistical and Nonlinear Physics

1. V. Ginzburg
2. Pavel Etingof
3. Y. Berest
4. I. Gordon
5. J. T. Stafford
6. G. Bellamy
7. Osamu Iyama
8. I. Losev

Citations in the corpus

• Finite-dimensional representations of rational Cherednik algebras (2002, background): “As was pointed out in [4], this allows to classify finite-dimensional representations of Hc(Sn) (i.”