Useful books
I will add more comments about these books throughout the term as I get a chance to read through more of them. I'm sure you can find PDFs of all of these on Library Genesis (but you didn't hear it from me).
- Bump, Lie Groups.
A bit more advanced, and seems to make more use of analysis. He covers a lot of fairly technical and powerful things that other authors like to omit.
- Fulton and Harris, Representation Theory: A First Course.
One of my primary references for preparing the talks. Gives a very nice treatment of the semisimple theory with lots of fully worked examples. On the other hand, they will not spoonfeed you every detail; you do need to think a bit for yourself. Also, it's written by two prominent algebraic geometers, so they give very interesting geometric perspectives on things.
- Gilmore, Lie Groups, Physics, and Geometry.
Seems to be written for physicists, mainly. A lot of explicit coordinatizations, parametrizations, and calculations. Some mathematical errors. However, it can be useful to get some intuition.
- Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction.
Seems quite friendly so far; if you are new to representation theory, Chapter 4 of this book will probably be helpful. He doesn't work as many examples as Fulton and Harris do, but you can tell that representations of Lie groups are what he really cares about.
- Harvey, Spinors and Calibrations.
- Humphreys, Introduction to Lie Algebras and Representation Theory.
More difficult and terse text. Haven't read too much of it just yet.
- Lawson and Michelsohn, Spin Geometry.
The first chapter is a good reference for Clifford algebras and spin representations. There is also a fair amount of index theory here.
- Varadarajan, Lie Groups, Lie Algebras, and their Representations.
Same story as above. This seems like a pretty authoritative reference on all of this stuff, although it is also a bit dry.
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