Related papers: Simple Finite Non-Abelian Flavor Groups
It is shown that it is possible to create successful models of flavor for both quarks and leptons using the discrete non-abelian group $T^{\prime}$ by itself. Two simple realizations are presented that can be used as the starting point for…
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…
Finite groups are said to be isospectral if they have the same sets of element orders. A finite nonabelian simple group $L$ is said to be almost recognizable by spectrum if every finite group isospectral to $L$ is an almost simple group…
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
We study infinite groups interpretable in power bounded $T$-convex, $V$-minimal or $p$-adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups)…
The neutrino oscillation data are well explained by the tri-bimaximal pattern. Recently a paper appeared showing that also the bimaximal pattern could be a very good starting point in order to describe the lepton mixing. In this paper I…
Four $SU(5)$ $N=1$ supersymmetric models which exhibit $S_3$ and/or $Z_N$ symmetries are studied, that are finite to two or all loops, and their corresponding mass matrices. The first is an all-loop finite model based on an $S_3\times…
Building on the classification of modules for algebraic groups with finitely many orbits on subspaces, we determine all faithful irreducible modules for simple and maximal-semisimple connected algebraic groups that are orthogonal and have…
Recent atmospheric and solar neutrino experiments suggest that neutrinos have small but nonzero masses. They further suggest that mass eigenvalues have certain degree of hierarchical structures, and also some mixing angles are near-maximal…
A representation $\Phi: G \to \mathrm{GL}_n(\mathbb{F})$ of a finite group $G$ is called unisingular if the matrix $\Phi(g)$ admits $1$ as an eigenvalue for any $g\in G$. In this paper, we determine all the complex irreducible unisingular…
The gauge model with $SO(3)_{F}$ flavor symmetry and three Higgs triplets is studied. We show how the intriguing nearly degenerate neutrino mass and bi-maximal mixing scenario comes out naturally after spontaneous breaking of the symmetry.…
In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…
A result of D. Segal states that every complex irreducible representation of a finitely generated nilpotent group $G$ is monomial if and only if $G$ is abelian-by-finite. A conjecture of A. N. Parshin, recently proved affirmatively by I.V.…
We study a new flavor symmetric model with non-Abelian discrete symmetry T_{13}. The T_{13} group is isomorphic to Z_{13} \rtimes Z_3, and it is the minimal group having two complex triplets as the irreducible representations. We show that…
The neutrino oscillation data find a good approximation in the so-called tri-bimaximal pattern. Recently a paper appeared showing that also the bimaximal pattern, which is already ruled out by the measurements, could be a very good starting…
A systematic study of the flavor group $T^{'}$ is presented in terms of a specific model which extends the standard model symmetry to $[SU(3) \times SU(2) \times U(1)]_{(local)} \times [T^{'} \times Z_2 \times Z_2^{'} \times…
Four different neutrino mass sum-rules have been analyzed: these frequently arise in flavor symmetry models based on the groups A_4, S_4 or T', which are often constructed to generate tri-bimaximal mixing. In general, neutrino mass can be…
We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt(5) and SL_2(5) is a Beauville group. In particular, we settle a…
Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is…
We show how the nearly bi-maximal mixing scenario comes out naturally from gauged $SO(3)_{F}$ flavor symmetry via spontaneous symmetry breaking. An interesting relation between the neutrino mass-squared differences and the mixing angle,…