2010/06/30 by Walter Grimus, W. Grimus, Patrick Otto Ludl +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algorithm #Character (mathematics) #Character table #Combinatorics #Computation #Computer science #Conjugacy class #Dihedral group #Geometry #Group (periodic table) #Irreducible representation #Mathematics #Neutrino Physics Research #Particle physics theoretical and experimental studies #Physics #Principal (computer security) #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Series (stratigraphy) #Tensor (intrinsic definition) #hep-ph #hep-th
paper · pdf · doi:10.1088/1751-8113/43/44/445209
published as J.Phys.A43:445209,2010 · 43 pages, no figures; typos corrected, clarifications and references added, version matches publication in J. Phys. A
arxiv created 2010/09/14 · openalex publication_date 2010/10/13 · arxiv updated 2014/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.