Simple Finite Non-Abelian Flavor Groups

TL;DR

This paper explores the mathematical structure of two finite simple non-Abelian flavor groups, A_5 and PSL_2(7), which are relevant for understanding neutrino mixing patterns in particle physics.

Contribution

It provides a detailed analysis of the two finite simple groups with two- and three-dimensional irreducible representations, expanding the mathematical foundation for flavor symmetry models.

Findings

Analyzed the structure of A_5 and PSL_2(7) groups

Identified their irreducible representations relevant for flavor physics

Contributed to the mathematical tools for neutrino mixing models

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).