Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)

Details Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3) Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)

2010-02-11

arxiv.org/abs/1002.2348v1

Mathematics

Operator Algebras

38 pages, 21 figures

Scientific paper

We complete the computation of spectral measures for SU(3) nimrep graphs arising in subfactor theory, namely the SU(3) ADE graphs associated with SU(3) modular invariants and the McKay graphs of finite subgroups of SU(3). For the SU(2) graphs the spectral measures distill onto very special subsets of the semicircle/circle, whilst for the SU(3) graphs the spectral measures distill onto very special subsets of the discoid/torus. The theory of nimreps allows us to compute these measures precisely. We have previously determined spectral measures for some nimrep graphs arising in subfactor theory, particularly those associated with all SU(2) modular invariants, all subgroups of SU(2), the torus, SU(3), and some SU(3) graphs.

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