Fourier transform and the Verlinde formula for the quantum double of a finite group

Details Fourier transform and the Verlinde formula for the quantum double of a finite group Fourier transform and the Verlinde formula for the quantum double of a finite group

1999-04-07

arxiv.org/abs/math/9904029v2

J.Phys.A32:8539-8549,1999

Mathematics

Quantum Algebra

15 pages, small errors corrected and references added, version to appear in Journal of Physics A

Scientific paper

10.1088/0305-4470/32/48/313

A Fourier transform S is defined 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,Z). 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.

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