Simple Finite Non-Abelian Flavor Groups

Abstract

The recently measured unexpected neutrino mixing patterns have caused a resurgence of interest in the study of finite flavor groups with two- and three-dimensional irreducible representations. This paper details the mathematics of the two finite simple groups with such representations, the Icosahedral group A_5, a subgroup of SO(3), and PSL_2(7), a subgroup of SU(3).

42 pages, matches published version, references added

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• The Golden Ratio Prediction for the Solar Angle from a Natural Model with A5 Flavour Symmetry
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• A Minimal Model of Neutrino Flavor
• The D_4 flavor symmery in 3-3-1 model with neutral leptons
• Neutrino mixing with non-zero ${\theta }_{13}$ and CP violation in the 3-3-1 model based on $A_4$ flavor symmetry
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• On the finite subgroups of U(3) of order smaller than 512
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• Proton Hexality from an Anomalous Flavor U(1) and Neutrino Masses - Linking to the String Scale
• CP Symmetry and Lepton Mixing from a Scan of Finite Discrete Groups
• Systematic analysis of finite family symmetry groups and their application to the lepton sector
• Neutrino Mixing with Non-Zero ${\theta }_{13}$ and CP Violation in the 3-3-1 Model Based on $S_4$ Flavor Symmetry
• SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry
• Comments on the classification of the finite subgroups of SU(3)
• The Double Cover of the Icosahedral Symmetry Group and Quark Mass Textures
• On discrete Minimal Flavour Violation
• Family symmetries and alignment in multi-Higgs doublet models
• Discrete flavour symmetries for degenerate solar neutrino pair and their predictions
• Adjoint $SU(5)$ GUT model with $T_7$ flavor symmetry
• An A_5 Model of Four Lepton Generations
• Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing
• M-theory Cosmology, Octonions, Error Correcting Codes
• Neutrino masses, the $\mu$-term and ${\mathcal{P}\mathcal{SL}}_2(7)$
• The flavor problem and discrete symmetries
• On the characterization of the SU(3)-subgroups of type C and D
• Neutrino masses and mixing from flavour antisymmetry
• A Note on Embedding Nonabelian Finite Flavor Groups in Continuous Groups
• Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT
• Strong coupling, discrete symmetry and flavour
• Modular Invariant Models of Leptons at Level 7
• Froggatt-Nielsen models with a residual Z_4^R symmetry
• $\mathcal{C}\mathcal{P}$ violation with an unbroken $\mathcal{C}\mathcal{P}$ transformation
• Binary Icosahedral Flavor Symmetry for Four Generations of Quarks and Leptons
• Constraining Low-Scale Flavor Models with $(\mathbf{g}-2{)}_{\mathbf{\mu }}$ and Lepton Flavor Violation
• On Building superpotentials in F- GUTs
• The role of PSL(2,7) in M-theory: M2-branes, Englert equation and the septuples
• Ultraheavy resonances at the LHC: beyond the QCD background
• Phenomenological implications of a minimal F-theory GUT with discrete symmetry
• Discrete Flavour Symmetries from the Heisenberg Group
• Clebsch-Gordan coefficients of discrete groups in subgroup bases
• PSL(2,7) Representations and their relevance to Neutrino Physics
• Two groups 2^3.PSL_2(7) and 2^3:PSL_2(7) of order 1344
• LHC probes of the 10 TeV scale