Say I have an anyonic system modelled as a Chern-Simons system with group $G$. If the centre of $G$ is non-trivial, one may also study the system described by $G/\Gamma$, where $\Gamma$ is a discrete subgroup of $Z(G)$.
In a recent conference, I've heard people referring to this process as anyon condensation (or gauging the symmetry $\Gamma$): the spectrum of $G/\Gamma$ can be obtained by identifying some anyons of the spectrum of $G$. What I understood from the conference is that the spectrum of $G/\Gamma$ is the set of equivalence classes of $\Gamma$-orbits of the lines of $G$ that are neutral under $\Gamma$. My understanding is probably incorrect to some level, because I got the impression that the $\Gamma$-orbits were sometimes broken up into smaller orbits, according to some prescription that was not clear to me. I didn't get the chance to ask the speaker at the time, and I cannot find any clear description online. Thus, my question: how is the spectrum of $G/\Gamma$ related to that of $G$? What is the precise definition of anyon condensation, and how can we implement this process in practice?