In order to continue our discussion of symmetric functions it will be useful to have some group representation theory prerequisites, although I will use many of the results in the representation theory of the symmetric groups as black boxes. I had planned on using this post to discuss Frobenius reciprocity, but got so carried away with motivating it that this post now stands alone.

Today I’d like to discuss the representation theory of finite groups over . As these are strong assumptions, the resulting theory is quite elegant, but I always found the proofs a little unmotivated, so I’m going to try to use the categorical perspective to fix that. Admittedly, I don’t have much experience with this kind of thing, so this post is for my own benefit as much as anyone else’s. The main focus of this post is motivating the orthogonality relations.