Representations of Compact Lie Groups (Graduate Texts in Mathematics (98))
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- Publisher : Springer (March 1, 1985)
- Language : English
- Hardcover : 326 pages
- ISBN-10 : 3540136789
- ISBN-13 : 978-3540136781
- Item Weight : 3.13 pounds
- Dimensions : 6.14 x 0.75 x 9.21 inches
- Best Sellers Rank: #1,728,808 in Books (See Top 100 in Books)
- Customer Reviews:
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There aren't very many geometrically flavored books on lie groups; I can think of only this one and "Compact lie groups" by Sepanski. His book has a nicer treatment of harmonic analysis, but this one beats his in almost every other respect. Sepanski is often too concise.
Still, this book has a long way to go to be really great. Though you're not assumed to have a prior knowledge of lie groups (just smooth manifold theory), you're going to crash and burn without it. That's why I suggest John Lee's Introduction to Smooth Manifolds before taking on this book. It has the best preparation in elementary lie groups you'll ever hope to find. It'll prepare you for Brocker and Dieck. Even then, the book isn't incredibly well written.
In short, there is no really well-written text on lie groups from a geometric perspective, but this one's the best there is. I hope someone writes a better one eventually.