Related papers: Simple Finite Non-Abelian Flavor Groups

We explore the implications of symmetries that remain unbroken at the self-dual point $\tau=i$ in modular invariant theories. Assuming that (a) the three generations of lepton doublets transform as an irreducible representation of a finite…

Assuming that finite family symmetries are gauged, we derive discrete anomaly conditions for various non-Abelian groups. We thus provide new constraints for flavor model building, in which discrete non-Abelian symmetries are employed to…

The simultaneous study of top-down and bottom-up approaches to modular flavor symmetry leads necessarily to the concept of eclectic flavor groups. These are nontrivial products of modular and traditional flavor symmetries that exhibit the…

Over the last ten years tri-bimaximal mixing has played an important role in modeling the flavour problem. We give a short review of the status of flavour symmetry models of neutrino mixing. We concentrate on non-Abelian discrete…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

We construct a supersymmetric (SUSY) $SU(5)$ model with the flavor symmetry $S_4\times Z_3\times Z_4$. Three generations of adjoint matter fields are introduced to generate the neutrino masses via the combined type I and type III see-saw…

Recent progress in the application of finite groups to neutrino mass matrices is reviewed, with special emphasis on the tetrahedral symmetry A_4.

We analyze all possible extensions of the recently proposed minimal renormalizable SUSY SU(5) grand unified model with the inclusion of an additional A4 flavor symmetry. We find that there are five possible cases but only one of them is…

We construct new classes of self-similar groups : S-aritmetic groups, affine groups and metabelian groups. Most of the soluble ones are finitely presented and of type FP_{n} for appropriate n.

We analyze the phenomenological consequences of embedding a flavor symmetry based on the groups $A_5$ and CP in a supersymmetric framework. We concentrate on the leptonic sector, where two different residual symmetries are assumed to be…

As the 3-string braid group B(3) and the modular group PSL(2,Z) are both of wild representation type one cannot expect a full classification of all their finite dimensional simple representations. Still, one can aim to describe 'most'…

We consider the neutrino physics of models with a sequentially broken U(2) flavor symmetry. Such theories yield the observed pattern of quark and lepton masses, while maintaining sufficient degeneracies between superparticles of the first…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

We present a simple modification of the Altarelli-Feruglio $A_4$ flavor symmetry model using a minimal number of parameters congruous with the symmetries of the original theory. The resulting model is consistent with all presently known…

We present a novel procedure for identifying discrete, leptonic flavour symmetries, given a class of unitary mixing matrices. By creating explicit 3D representations for generators of residual symmetries in both the charged lepton and…

We motivate the usage of finite groups as symmetries of the Lagrangian. After a presentation of basic group-theoretical concepts, we introduce the notion of characters and character tables in the context of irreducible representations and…

We prove two results on some special generators of finite simple groups and use them to prove that every non-abelian finite simple group $S$ admits a non-congruence presentation (as conjectured in [CLT24]), and that if $S$ has a non-trivial…

We construct a supersymmetric theory of flavor based on the discrete gauge group (D_6)^2, where D_6 describes the symmetry of a regular hexagon under proper rotations in three dimensions. The representation structure of the group allows one…

Neutrino flavor mixing is explained within the recently proposed low-scale minimal linear seesaw model of neutrino mass generation, a variant of the standard linear seesaw led by a Dirac pair of extra sterile neutrinos which is odd under a…

We study neutrino masses and mixing in the context of flavor models with A4 symmetry, three scalar doublets in the triplet representation, and three lepton families. We show that there is no representation assignment that yields a…