The Flavor Group Delta(6n^2)
J. A. Escobar, Christoph Luhn

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.
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