Hello everyone. I need someone to explain a concept to me. I'm confused about how a type of particle can be a representation of a lie group. For example, I read that particles with half-integer spin j are a representation of the group SU(2), or that particles with charge q are a representation of U(1). But what is it about the group that the particle actually represents? Do the particles correspond to the generators? Or the group elements? What's the defining feature that a type of particle must have to be a representation of the group? If anyone can explain this in a way I can understand, I'd be eternally grateful!