The Flavor Group Delta(3n^2)

TL;DR

This paper explores the mathematical properties of the Delta(3n^2) group, a finite subgroup of SU(3), to understand its potential role in explaining neutrino mixing angles in particle physics.

Contribution

It provides a detailed mathematical analysis of Delta(3n^2), including conjugacy classes, character table, irreducible representations, and invariants, which was not previously comprehensively documented.

Findings

Derived conjugacy classes and character table of Delta(3n^2)

Constructed irreducible representations and their Kronecker products

Identified invariants relevant to flavor symmetry models

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.