What are the things one can expect to understand after studying the representation of a group? I have seen many answers on pages regarding the importance and philosophy of representation theory but I am unable to understand what good it will do as a short term goal (meaning I'm not interesting in things it will enable me to study later).
Suppose I have studied the representation of $SO(n)$ or $SU(n)$. What are the questions I will be able to answer about it that I can't (or not easily) without the knowledge of representation theory?
Edit: I don't understand why even after explaining that what I'm looking for is not available on that page, this question is marked as duplicate.
To quote, it says now that "This question was marked as an exact duplicate of an existing question." which according to me is rather absurd. I'd argue that this is much more specific and will benefit a lot of people getting introduced to the subject.
