Breaking classical Lie groups to finite subgroups – an automated approach

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 A4 and Δ(27) general analytical formulas are presented for the branching rules of arbitrary representations of their smallest Lie super-groups.