After 100 years of effort, the classification of all the finite subgroups of $$SU(3)$$ is yet incomplete. The most recently updated list can be found in Ludl (J Phys A Math Theory 44:255204, 2011), where the structure of the series $$(C)$$ and $$(D)$$ of $$SU(3)$$ -subgroups is studied. We provide a minimal set of generators for one of these groups which has order $$162$$ . These generators appear up to phase as the image of an irreducible unitary braid group representation issued from the Jones–Kauffman version of $$SU(2)$$ Chern–Simons theory at level $$4$$ . In light of these new generators, we study the structure of the group in detail and recover the fact that it is isomorphic to the semidirect product $$\mathbb Z _9\times \mathbb Z _3\rtimes S_3$$ with respect to conjugation.
Quantum Information Processing – Springer Journals
Published: Feb 23, 2013
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