Spectral measures for \(G_2\). II: Finite subgroups. (English) Zbl 1493.22013
Summary: Joint spectral measures associated to the rank two Lie group \(G_2\), including the representation graphs for the irreducible representations of \(G_2\) and its maximal torus, nimrep graphs associated to the \(G_2\) modular invariants have been studied. In this paper, we study the joint spectral measures for the McKay graphs (or representation graphs) of finite subgroups of \(G_2\). Using character theoretic methods we classify all non-conjugate embeddings of each subgroup into the fundamental representation of \(G_2\) and present their McKay graphs, some of which are new.
For Part I, see [the authors, Commun. Math. Phys. 337, No. 3, 1161–1197 (2015; Zbl 1321.46067)].
For Part I, see [the authors, Commun. Math. Phys. 337, No. 3, 1161–1197 (2015; Zbl 1321.46067)].
MSC:
| 22E46 | Semisimple Lie groups and their representations |
| 46L37 | Subfactors and their classification |
Citations:
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