The Flavor Group Delta(6n^2)

TL;DR

This paper systematically analyzes the mathematical structure of the Delta(6n^2) groups, which are used in flavor physics models, by determining their conjugacy classes, irreducible representations, and tensor product rules.

Contribution

It provides a comprehensive classification and detailed representation theory of the Delta(6n^2) groups for arbitrary n, aiding model building in particle physics.

Findings

Determined conjugacy classes for all Delta(6n^2) groups.

Derived irreducible representations and their tensor products.

Calculated Clebsch-Gordan coefficients for these groups.

Abstract

Many non-Abelian finite subgroups of SU (3) have been used to explain the flavor structure of the Standard Model. In order to systematize and classify successful models, a detailed knowledge of their mathematical structure is necessary. In this paper we shall therefore look closely at the series of finite non-Abelian groups known as Delta(6n^2), its smallest members being S3 (n = 1) and S4 (n = 2). For arbitrary n, we determine the conjugacy classes, the irreducible representations, the Kronecker products as well as the Clebsch-Gordan coefficients.