# 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.
## Outline:

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.

**Instructor:** Dan Christensen
**E-mail:** jdc@uwo.ca
**Office:** Middlesex 103b.
**Office Phone:** 661-2111 x86530.
**Office Hours:** after class or by appointment.
**Class times and location:** Tuesdays and Thursdays,
10:30 to 12:30; MC107. **Starts Jan 16.**
**Prerequisites:** Group theory and linear algebra,
or permission of instructor.

**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
amazon.ca.
You can view some of the introductory pages (including the table
of contents) at
amazon.com.

**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.

Back to Dan Christensen's home page.

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