Breaking classical Lie groups to finite subgroups - an automated approach

TL;DR

This paper introduces an automated method using a Mathematica package to decompose classical Lie group representations into finite subgroup representations, providing both computational tools and analytical formulas for specific cases.

Contribution

It presents a new automated approach and software for deriving branching rules from classical Lie groups to finite subgroups, including analytical formulas for certain low order groups.

Findings

Developed a Mathematica package for decomposition calculations

Provided analytical formulas for A4 and Delta(27) groups

Enabled systematic analysis of Lie group to finite subgroup representations

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.