# Fluxes on a finite group $G$

So I've been studying about topological quantum computation and I have a few questions I haven't been able to solve. The first one is why fluxes take values on a finite group $$G$$? Does it have to do with the boundaries of the 2-dimensional space we work? The second question is, can fluxes take values on any finite group $$G$$ we want? And the last one is why the charges are the irreducible representations of the group? Any paper or bibliography solving my questions would be much appreciated.

• I think your question could use some clarification/context. What "fluxes" are you talking about? It sounds like you are asking about gauge theories specifically, but that is not very clear from the question. Gauge theories of finite gauge group are one example of topological phases in 2-D, but there are other ones too. – Dominic Else May 17 '19 at 14:27
• In Preskill's lecture notes he refers that if we a consider a two dimensional nonabelian superconductor then there exist particles that carry magnetic flux that takes values in a nonabelian finite group G and the charges are the unitary irreducible representations of the group G. And then he makes a complete analysis using this as a fact. My question is why the fluxes take values on G? – Giannis Kolotouros May 17 '19 at 14:34