Truncated Fusion Rules for Supergroups

In the '70s, physicists introduced a new type of symmetry – supersymmetry – to address some unresolved issues in particle physics models. Its mathematical foundations involve the representation theory of the associated symmetry groups, called supergroups. Our aim is to understand fusion rules, which describe how a combination of two physical systems can be broken down into more fundamental building blocks. Although the answer is largely unknown, we can get approximate answers in some cases.