2001/10/01 by Ivan Cherednik, Cherednik, Ivan
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #FOS: Mathematics #Molecular spectroscopy and chirality #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.math/0110024
106 pgs, LaTeX, to appear in Inventiones Math. A latex variant with some changes in Intro and Ch.7
openalex publication_date 2001/10/01 · arxiv created 2002/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.