Breaking classical Lie groups to finite subgroups - an automated approach

Abstract

The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character formula. For some low order finite groups including $A_4$ and $\Delta (27)$ general analytical formulas are presented for the branching rules of arbitrary representations of their smallest Lie super-groups.

21 pages, minor changes, matches published version

References in corpus (9)

• Symmetries and Strings in Field Theory and Gravity
• Stringy origin of non-Abelian discrete flavor symmetries
• Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models
• Discrete symmetries in the three-Higgs-doublet model
• Measurement of the Z/gamma* + b-jet cross section in pp collisions at 7 TeV
• Non-Abelian Discrete Groups from the Breaking of Continuous Flavor Symmetries
• Lepton Mixing in $A_5$ Family Symmetry and Generalized CP
• Anomaly Conditions for Non-Abelian Finite Family Symmetries
• Symmetries of symmetries and geometrical CP violation

Cited by in corpus (3)

• CP and other Symmetries of Symmetries
• $\mathcal{C}\mathcal{P}$ violation with an unbroken $\mathcal{C}\mathcal{P}$ transformation
• Simultaneous Block Diagonalization of Matrices of Finite Order