Representation Theory: A First Course

Graduate Texts in Mathematics #129

by William Fulton, Joe Harris

The primary goal of these lectures is to introduce a beginner to the finite-dimensional representations of Lie groups and Lie algebras. Intended to serve non-specialists, the concentration of the text is on examples. The general theory is developed sparingly, and then mainly as useful and unifying language to describe phenomena already encountered in concrete cases. The book begins with a brief tour through representation theory of finite groups, with emphasis determined by what is useful for Lie groups. The focus then turns to Lie groups and Lie algebras and finally to the heart of the course: working out the finite dimensional representations of the classical groups. The goal of the last portion of the book is to make a bridge between the example-oriented approach of the earlier parts and the general theory.

Genres: Mathematics, Textbooks, Stem, Physics, Theory

566 pages, Paperback

First published October 22, 1991

Reviews

[Joseph]

This is a really good book.

[J]

It was nice for a while because of all the concrete examples, but why doesn't the book prove anything? Even the proofs that are there are often kind of sloppy and miss important details. It's good for getting the general feel for the representation theory of semisimple Lie algebras (the sl3 example is really nice and you really get a great overall picture from studying it) but not good as a standalone textbook, you'll need another book to give you understandable proofs.

[Ethan Jensen]

There’s no way this is a ‘first course’. It does have great appendices to help though. It is the undisputed best book on representation theory, but I think it’s possible for someone to come along and do better.

[Matthew Zhang]

a bit off topic but very well written :)

[Lulu]

Lie groups, Lie algebras and their representations