Representation Theory, Math 562b, Spring 2007

This course will study the representation theory of finite groups and Lie groups, including some applications to physics. Only a basic background in group theory and linear algebra will be assumed.


The choice of topics will depend on the interests of the students. Here is a rough idea:

Mathematical topics: a review of group theory, representations, irreducibility, complete reducibility, Schur's lemma, character theory, induced representations, Lie groups, Haar measure, the Peter-Weyl theorem, and Lie algebras.

Examples: cyclic groups, dihedral groups, symmetric groups, SU(2), SO(3), SL(2,C), SO(3,1), the Poincare group, SU(n), GL(n), etc.

Physical topics: molecular vibrations, radiation, exchange forces, the hydrogen atom, wave equations, quarks, TQFTs (including knot invariants) and quantum gravity.

The course will meet for 4 hours each week, for a total of 10 weeks, starting Tuesday, January 16. The 10 weeks won't be consecutive, as I will be away from time to time.

Text: The text is Shlomo Sternberg's Group Theory in Physics. The library copy is on 2-hour reserve. I have asked the book store to order 5 copies, but I don't know when they will arrive. Some used copies are available via You can view some of the introductory pages (including the table of contents) at

Homework: Homework will be due roughly every two weeks.

Presentations: In the second half of the semester, each student will give a presentation on a topic related to the course.

Exam: There will be a final exam at the end of the course.

Evaluation: Evaluation will be based upon homework, presentations and the final exam.

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