Comparing Books on Lie Groups: Representations & Compact Lie Groups

[mrandersdk]

I'm taking a course on Lie Groups and the Representations. We are using the book: Representations of compact Lie Groups by Bröcker and Dieck, and I find it very unorganized and sometimes sloppy. Can anybody recommend a very clear and rigorous book, where it is not prove by example, "it is easily seen", etc.

I have taking a course on manifolds and riemannian geometry so I'm not a complete novice in the field of differential geometry.

I've been thinking about the book Compact Lie Groups by Sepanski, anybody got a comment on this book?

Thanks in advance.

 

[mathwonk]

I know next to nothing about the topic, but I am a professional mathematician and thus understand the value of expert treatments.

hence i would suggest looking at the books by great experts like chevalley, weyl, serre.

such books tend to be hard and condensed , but well organized and authoritative.

 

[cristo]

Here are a couple of links to posts in the past discussing this topic:
https://www.physicsforums.com/showpost.php?p=1554729&postcount=6
https://www.physicsforums.com/showpost.php?p=1532176&postcount=7