# Introduction to Representation theory of Algebraic Groups

This is a very basic and most definitively a naive question but coming from a student it is probably OK.

I am trying to learn representation theory of (linear) algebraic groups and looking for a an easy resource. The books and notes which I have come across start with extensive knowledge of algebraic geometry (which is essential for a comprehensive treatment) but coming from a weak background of mathematics by the time you absorb all that you are exhausted.

I am wondering if there is another way to get into representation theory of algebraic groups without worrying too much about algebraic geometry part. We have tried to go through the famous books (Humphreys, Springer, Borel), although excellent but too much for a beginner only interested in representation theory part to start with.

Any help will be highly appreciated.

• "Representation theory" is a fairly large topic, but for algebraic groups in characteristic 0 it's usually much easier to start with the mostly equivalent classical (finite dimensional) representation theory of semisimple Lie algebras. For this there are a number of self-contained books including the text by Fulton and Harris. More ambitious books by Goodman-Wallach, Onishnik-Vinberg combine this with some study of the groups. The problems in prime characteristic go deeper and are less understood, so it's unclear where you draw a line. – Jim Humphreys Sep 28 '16 at 13:23
• P.S. The transliteration is actually "Onishchik". – Jim Humphreys Sep 28 '16 at 13:38
• You're going to have to learn the general theory eventually, but a good first overview that avoids technicalities is Carter-Segal-MacDonald's "Lectures on Lie Groups and Lie Algebras". It contains three sets of lecture notes; the third is on linear algebraic groups and the first is on the representation theory of Lie algebras. Given your interests, I suppose that you could skip the chapter on the representation theory of compact Lie groups. – Andy Putman Sep 28 '16 at 13:59