I recently finished a course in representation theory, and while I learned a lot from it, I know that there's a lot more in the subject that I missed. For the course we used Fulton and Harris as a reference, but really only took exercises from it; the course notes were the professor's own notes. And having read through Fulton and Harris a little, I realize that it's pretty hard to learn from.
So I'm looking for a text on representation theory geared toward early graduate students (or even advanced undergraduates) that have NO experience in the subject whatsoever. Preferably with lots of examples, computations, and loads of exercises that is generally considered good for self-study. I want to start at the beginning again and really develop my intuition and fill in gaps in my knowledge. My preference also is to work with finite groups, but I assume most books at the level I want cover finite groups at least some, and this is certainly not a deal-breaker. Anyone have any suggestions?
Perhaps that list narrows things too much, but anything that has a sufficient number of these qualities should do. Thank you!
Best Answer
I really like Huppert's Character Theory of Finite Groups. Isaacs book under the same name is also very good, and probably easier to come by; it is about $10 on amazon. I read both of these as an undergraduate (and I hated Fulton and Harris).
There are a few differences between the two. Huppert was written after Isaacs and contains many more results about character degrees, especially where they tie into Huppert's $\sigma$-$\rho$ conjecture. Another thing I like about Huppert (and this is just a personal preference) is that it has slight module-theoretic bias, whereas Isaacs is entirely characters. Huppert also contains more elaborate examples. On the other hand, Isaacs covers projective representations in greater detail, and contains sections on Schur multipliers and Brauer theory, both of which are completely absent in Huppert. Both books have fantastic exposition.