A Clarifying Fradkin's Terminology on Quantum Numbers of Gauge Groups

[paralleltransport]

TL;DR

I'd like to clarify some terminology

Hi, I'd like to clarify the following terminology
(Fradkin, Quantum Field Theory an integrated approach)

"carry the quantum numbers of the representation of the gauge group":
Does the author basically mean that the wilson loop is a charged operator, in a sense that it transforms non-trivially under gauge transformation:
W -> U(x) W U(x)^{-1}

Furthermore, the fact that the wilson loop transforms under the fundamental representation means that it is just a N x N matrix for SU(N) gauge field and transforms according the conjugation law above?

Finally, the so called "quantum numbers" are then just the charges associated with each gauge group generator?

 

[vanhees71]

Yes, I think that's what Fradkin means.