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 A4 and Δ(27) general analytical formulas are presented for the branching rules of arbitrary representations of their smallest Lie super-groups.
Highlights
The Standard Model of particle physics (SM) provides a highly accurate description of Nature
After clarifying some notational issues, the Weyl character formulas for the classical Lie groups are presented in two formulations due to Weyl, which are for the present purposes more useful than the general formula mentioned before
Non-abelian finite symmetries are popular tools in model building. They can originate from spontaneously broken continuous symmetries, thereby evading the conjectured violation of global symmetries by gravitational effects
Summary
The Standard Model of particle physics (SM) provides a highly accurate description of Nature. Both approaches cannot be generalised to larger Lie group representations or larger rank Lie groups In another approach that highlights the connection between spontaneous and explicit symmetry breaking, Merle and Zwicky [17] used an algorithm based on group invariants and provided a MATHEMATICA package implementing the algorithm for SU(3). This is not generalised, and the method relies on somewhat advanced notions of invariant theory.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
