Representation theory by virtue I feel has more angles than most branches of mathematics, but your definition isn't off at all. I tend to focus in particular in

Representation theory by virtue I feel has more angles than most branches of mathematics, but your definition isn't off at all. I tend to focus in particular in terms of information theory which is where the combinatorial and symmetric groups, to name a few sides of representation theory, are of particular interest, but isn't the entire picture by a long shot.