A new set of generators and a physical interpretation for the SU(3) finite subgroup D(9,1,1;2,1,1)

作者：Bauer Bela; Levaillant Claire^*

来源：Quantum Information Processing, 2013, 12(7): 2509-2521.

DOI：10.1007/s11128-013-0544-6

• SU(3) finite subgroups
• Unitary braid groups representations
• Anyonic systems

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 Z(9) x Z(3) x S-3 with respect to conjugation.

• 出版日期2013-7