PSL(2,7) Representations and their relevance to Neutrino Physics

TL;DR

This paper derives and analyzes the three-dimensional unitary representations of PSL(2,7), exploring their potential to explain neutrino mixing angles consistent with experimental data.

Contribution

It provides the first detailed derivation of PSL(2,7) representations and connects them to neutrino flavor mixing phenomenology.

Findings

Representations reproduce observed neutrino mixing angles.

Group elements exhibit a latin square pattern.

Analytical expressions for group elements are provided.

Abstract

The investigation of the role of finite groups in flavor physics and particularly, in the interpretation of the neutrino data has been the subject of intensive research. Motivated by this fact, in this work we derive the three-dimensional unitary representations of the projective linear group PSL_2(7). Based on the observation that the generators of the group exhibit a latin square pattern, we use available computational packages on discrete algebra to determine the generic properties of the group elements. We present analytical expressions and discuss several examples which reproduce the neutrino mixing angles in accordance with the experimental data.