Principal series of finite subgroups of SU(3)

Author(s)
Walter Grimus, Patrick Otto Ludl
Abstract

We attempt to give a complete description of the 'exceptional' finite subgroups Σ(36 × 3), Σ(72 × 3) and Σ(216 × 3) of SU(3), with the aim to make them amenable to model building for fermion masses and mixing. The information on these groups which we derive contains conjugacy classes, proper normal subgroups, irreducible representations, character tables and tensor products of their three-dimensional irreducible representations. We show that, for these three exceptional groups, usage of their principal series, i.e. ascending chains of normal subgroups, greatly facilitates the computations and illuminates the relationship between the groups. As a preparation and testing ground for the usage of principal series, we study first the dihedral-like groups Δ(27) and Δ(54) because both are members of the principal series of the three groups discussed in the paper.

Organisation(s)
Particle Physics
Journal
Journal of Physics A: Mathematical and General
Volume
43
No. of pages
35
ISSN
0305-4470
DOI
https://doi.org/10.1088/1751-8113/43/44/445209
Publication date
2010
Peer reviewed
Yes
Austrian Fields of Science 2012
103036 Theoretical physics
Portal url
https://ucrisportal.univie.ac.at/en/publications/principal-series-of-finite-subgroups-of-su3(e726efd8-f316-4ceb-920d-f932761e8493).html