[Math] searching for text for studying representation theory

reference-requestrt.representation-theorytextbook-recommendation

I'm a graduate student studying algebraic geometry.
Recently, When I studying Hodge theory, I saw sl2-representation is used in Hodge theory.
So I think that studying representation theory may be helpful for me.
Can you recommand me some good text for studying representation theory, focused on materials helpful for algebraic geometry, and not so difficult to read.

Best Answer

I would recommend Introduction to Lie Algebras and Representation Theory by Humphreys. It covers all the basics of Lie algebras and their representations, though mostly in characteristic 0 and over an algebraically closed field. But then, going into any depth with the theory without these assumptions requires a lot of additional work anyway, and knowing the theory for this nice case is a good start.