%0 Generic %1 Ishimori2010 %A Ishimori, Hajime %A Kobayashi, Tatsuo %A Ohki, Hiroshi %A Okada, Hiroshi %A Shimizu, Yusuke %A Tanimoto, Morimitsu %D 2010 %K imported %T Non-Abelian Discrete Symmetries in Particle Physics %U http://arxiv.org/abs/1003.3552 %X Non-Abelian discrete symmetires have been playing an important role in the particle physics. In this article, we review pedagogically non-Abelian discrete groups. We show group-theoretical aspects for many concrete groups, such as representations and their tensor products. We discuss 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. We explain how to derive conjugacy classes, characters, representations and tensor products for these groups. We also present typical flavor models by using $A_4$, $S_4$ and $\Delta (54)$ groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetries. We discuss these breaking patterns of the non-Abelian discrete groups. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach. We show anomaly-free conditions explicitly for the above concrete groups.

@misc{Ishimori2010, abstract = { Non-Abelian discrete symmetires have been playing an important role in the particle physics. In this article, we review pedagogically non-Abelian discrete groups. We show group-theoretical aspects for many concrete groups, such as representations and their tensor products. We discuss 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. We explain how to derive conjugacy classes, characters, representations and tensor products for these groups. We also present typical flavor models by using $A_4$, $S_4$ and $\Delta (54)$ groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetries. We discuss these breaking patterns of the non-Abelian discrete groups. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach. We show anomaly-free conditions explicitly for the above concrete groups. }, added-at = {2010-03-19T09:41:59.000+0100}, author = {Ishimori, Hajime and Kobayashi, Tatsuo and Ohki, Hiroshi and Okada, Hiroshi and Shimizu, Yusuke and Tanimoto, Morimitsu}, biburl = {https://www.bibsonomy.org/bibtex/22df0e87e3055571744c3ec1e63ddbe4a/tamal}, description = {Non-Abelian Discrete Symmetries in Particle Physics}, interhash = {3bed9dfd14a0b333de8badd93d0aa69f}, intrahash = {2df0e87e3055571744c3ec1e63ddbe4a}, keywords = {imported}, note = {cite arxiv:1003.3552 Comment: 177 pages, 8 figures}, timestamp = {2010-03-19T09:41:59.000+0100}, title = {Non-Abelian Discrete Symmetries in Particle Physics}, url = {http://arxiv.org/abs/1003.3552}, year = 2010 }