I have only very little knowledge of group theory and representation theory. There is a lot to learn, so I wondered what are the final contributions to physical understanding from representation theory? I'd like to find some less abstract results. For example that the mass is the Casimir invariant of the Poincare group seems like a useful insight, but I don't understand the details :) Does representation theory help to understand the law of quantum mechanics or general relativity? Or does it just predict the existence of some "things" and restrict the form of physical laws?