Principal series of finite subgroups of SU(3)

Autor(en)

Walter Grimus, Patrick Otto Ludl

Abstrakt

We attempt to give a complete description of the 'exceptional' finite subgroups Σ(36 × 3), Σ(72 × 3) and Σ(216 × 3) of SU(3), with the aim to make them amenable to model building for fermion masses and mixing. The information on these groups which we derive contains conjugacy classes, proper normal subgroups, irreducible representations, character tables and tensor products of their three-dimensional irreducible representations. We show that, for these three exceptional groups, usage of their principal series, i.e. ascending chains of normal subgroups, greatly facilitates the computations and illuminates the relationship between the groups. As a preparation and testing ground for the usage of principal series, we study first the dihedral-like groups Δ(27) and Δ(54) because both are members of the principal series of the three groups discussed in the paper.

Organisation(en)

Teilchenphysik

Journal

Journal of Physics A: Mathematical and General

Band

43

Anzahl der Seiten

35

ISSN

0305-4470

DOI

https://doi.org/10.1088/1751-8113/43/44/445209

Publikationsdatum

2010

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/principal-series-of-finite-subgroups-of-su3(e726efd8-f316-4ceb-920d-f932761e8493).html