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.