1999/04/30 by T. H. Koornwinder, Tom H. Koornwinder, Bernd J. Schroers +4 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #hep-th #math-ph #math.MP #math.QA #msc:16W30 #msc:20Cxx #msc:81R50
paper · pdf · doi:10.1088/0305-4470/32/48/313
published as J.Phys.A32:8539-8549,1999 · 15 pages, small errors corrected and references added, version to appear in Journal of Physics A
arxiv created 1999/11/10 · openalex publication_date 1999/11/17 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/30
We define a Fourier transform S for the quantum double D ( G ) of a finite group G . Acting on characters of D ( G ), S and the central ribbon element of D ( G ) generate a unitary matrix representation of the group SL(2, ). The characters form a ring over the integers under both the algebra multiplication and its dual, with the latter encoding the fusion rules of D ( G ). The Fourier transform relates the two ring structures. We use this to give a particularly short proof of the Verlinde formula for the fusion coefficients.