Math 619 -- Lie Algebras and Lie Groups

Spring Semester, 2008

Tuesday, Thursday, 9-10:15 am, Krieger 304

Here is a rough syllabus:

• Lie groups & Lie algebras: definitions & examples, Ad & ad, compact/noncompact/complexification, semisimplicity
• Representations: semisimplicity & Schur's lemma, characters, Peter-Weyl theorem, examples
• Maximal tori: Cartan subalgebras, Weyl groups
• Root systems: Stiefel & Dynkin diagrams, classification of complex semisimple Lie algebras
• Characters & weights: Weyl character formula, representations of U(n) and SU(n)

The recommended text is: Representations of Compact Lie Groups (Graduate Texts in Mathematics)
by T. Bröcker, T.tom Dieck, Springer; 1st ed. 1985. 3rd printing edition (July 12, 2003)
ISBN-10: 3540136789
ISBN-13: 978-3540136781

Here are some lecture notes. They will be updated as the course continues. Please send corrections.

Problem Sets: #1 , #2 , #3 , #4 , #5