Non-Abelian Discrete Symmetries in Particle Physics

Understand

We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics.

• We show group-theoretical aspects for many concrete groups, such as representations, their tensor products.
• We explain how to derive, conjugacy classes, characters, representations, and tensor products for these groups (with a finite number).
• We discussed them explicitly for $S_N$, $A_N$, $T'$, $D_N$, $Q_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$, $T_7$, $\Sigma(3N^3)$ and $\Delta(6N^2)$, which have been applied for model building in the particle physics.