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Evans, David E.; Pugh, Mathew

Spectral measures and generating series for nimrep graphs in subfactor theory. II: \(SU(3)\). (English) Zbl 1217.46041

Commun. Math. Phys. 301, No. 3, 771-809 (2011).
Summary: We complete the computation of spectral measures for \(SU(3)\) nimrep graphs arising in subfactor theory, namely, the \({SU(3) \mathcal{ADE}}\) 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 \({\mathbb{T}^2,\,SU(3)}\), and some \(SU(3)\) graphs.
[For part I, see Commun. Math. Phys. 295, No. 2, 363–413 (2010; Zbl 1210.46046).]

Cited in 1 Review
Cited in 6 Documents

MSC:

46L37 Subfactors and their classification

Keywords:

spectral measures; nimrep graphs; subfactor

Citations:

Zbl 1210.46046
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Full Text: DOI arXiv

References:

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