The Flavor Group Delta(3n^2)

Abstract

The large neutrino mixing angles have generated interest in finite subgroups of SU(3), as clues towards understanding the flavor structure of the Standard Model. In this work, we study the mathematical structure of the simplest non-Abelian subgroup, Delta(3n^2). Using simple mathematical techniques, we derive its conjugacy classes, character table, build its irreducible representations, their Kronecker products, and its invariants.

29 pages, one table, typos corrected, matches published version

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• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• CP and Discrete Flavour Symmetries
• Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
• Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models
• Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups
• Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models
• Near Tribimaximal Neutrino Mixing with Delta(27) Symmetry
• The Flavor Group Delta(6n^2)
• S4 as a natural flavor symmetry for lepton mixing
• Trimaximal TM1 neutrino mixing in S4 with spontaneous CP violation
• Golden Ratio Neutrino Mixing and $A_5$ Flavor Symmetry
• A SUSY A4 model for fermion masses and mixings
• On the origin of neutrino flavour symmetry
• Finite flavour groups of fermions
• A common origin of fermion mixing and geometrical CP violation, and its test through Higgs physics at the LHC
• Two Loop Radiative Seesaw Model with Inert Triplet Scalar Field
• A4 models of tri-bimaximal-reactor mixing
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• Dirac neutrinos from flavor symmetry
• Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries
• Simple Finite Non-Abelian Flavor Groups
• Resonant enhancement in leptogenesis
• A new family symmetry for SO(10) GUTs
• Geometrical CP violation from non-renormalisable scalar potentials
• Lepton Mixing Parameters from $\Delta (48)$ Family Symmetry and Generalised CP
• Geometrical CP Violation
• Tribimaximal Mixing From Small Groups
• A(4) Flavor Symmetry Model for Dirac-Neutrinos and Sizable U(e3)
• Minimal see-saw model predicting best fit lepton mixing angles
• Predicting Lepton Flavor Mixing from $\Delta (48)$ and Generalized CP Symmetries
• Principal series of finite subgroups of SU(3)
• Flavor and CP symmetries for leptogenesis and 0nubb decay
• CP Violation in the Lepton Sector and Implications for Leptogenesis
• Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian's approach
• Geometrical CP violation in multi-Higgs models
• Lepton Flavor Model from Delta(54) Symmetry
• 5D and 6D SCFTs from ${\mathbb{C}}^3$ orbifolds
• On the finite subgroups of U(3) of order smaller than 512
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• Three-Higgs-doublet model with $A_4$ symmetry
• Quark and lepton mixing angles with a dodeca-symmetry
• Proton Hexality from an Anomalous Flavor U(1) and Neutrino Masses - Linking to the String Scale
• Natural Vacuum Alignment from Group Theory: The Minimal Case
• SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry
• Generalized CP and $\Delta (3n^2)$ Family Symmetry for Semi-Direct Predictions of the PMNS Matrix
• Invariant approach to CP in unbroken $\Delta (27)$
• Quark and Lepton Mixing Patterns from a Common Discrete Flavor Symmetry with Generalized CP
• Tri-bi-maximal mixing in viable family symmetry unified model with extended seesaw
• Mapping out SU(5) GUTs with non-Abelian discrete flavor symmetries
• Comments on the classification of the finite subgroups of SU(3)
• The symmetry approach to quark and lepton masses and mixing
• Resonant Dirac leptogenesis on throats
• A Unified Model of Quarks and Leptons with a Universal Texture Zero
• The Double Cover of the Icosahedral Symmetry Group and Quark Mass Textures
• Delta(54) Flavor Model for Leptons and Sleptons
• Fermion masses and mixing in $\Delta (27)$ flavour model
• On discrete Minimal Flavour Violation
• Stitching an Asymmetric Texture with ${\mathcal{T}}_{13}\times {\mathcal{Z}}_5$ Family Symmetry
• Discrete flavour symmetries for degenerate solar neutrino pair and their predictions
• CP-odd invariants for multi-Higgs models: applications with discrete symmetry
• Leptonic mixing, family symmetries, and neutrino phenomenology
• Minima of multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Non-Abelian Discrete Flavor Symmetries
• Delta(54) flavor phenomenology and strings
• A three-parameter neutrino mass matrix with maximal CP violation
• Deviations from Tribimaximal Neutrino Mixing using a Model with $\Delta (27)$ Symmetry
• Unified model of fermion masses with Wilson line flavor symmetry breaking
• A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios
• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Quasi-degenerate neutrinos and tri-bi-maximal mixing
• Non-Abelian Discrete Flavor Symmetries on Orbifolds
• The flavor problem and discrete symmetries
• The other variants of mixed $\mu$-$\tau$ symmetry
• On the characterization of the SU(3)-subgroups of type C and D
• Flavour and CP symmetries in the inverse seesaw
• Quasi-degenerate neutrinos and tri-bi-maximal mixing
• Neutrino masses and mixing from flavour antisymmetry
• Flavor Delta(54) in SU(5) SUSY Model
• A Note on Embedding Nonabelian Finite Flavor Groups in Continuous Groups
• Revisiting the Dirac Nature of Neutrinos in the Light of $\Delta (27)$ and Cyclic Symmetries
• Strong coupling, discrete symmetry and flavour
• Family symmetries and the origin of fermion masses and mixings
• Lepton mixing from the hidden sector
• Constrained Neutrino Mass Matrix and Majorana Phases
• Low-scale leptogenesis with flavour and CP symmetries
• Flavor origin of R-parity
• Implications of the Muon g-2 result on the flavour structure of the lepton mass matrix
• Relative scale separation in orbifolds of $S^2$ and $S^5$
• Pocket Formulae for Non-Abelian Discrete Anomaly Freedom
• Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
• Neutrino tri-bi-maximal mixing through sequential dominance
• Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)
• Systematic analysis of 3HDM symmetries
• Searching exotic Higgs bosons at the LHC
• Revisiting the Universal Texture Zero of Flavour: a Markov Chain Monte Carlo Analysis
• Flavor's Delight
• Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models