- Fourier transform and the Verlinde formula for the quantum double of a finite group
- Journal of Physics. A, Mathematical and General
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Institute for Theoretical Physics Amsterdam (ITFA)
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 $SL(2,Z)$. 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.
- go to publisher's site
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.