# Representation Theory, Math 562a, Summer 2003

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: the symmetric groups,
SU(2), SO(3), SL(2,C), SO(3,1), the Poincare group, SU(n), GL(n)
and various finite groups.

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.

**Instructor:** Dan Christensen
**E-mail:** jdc@uwo.ca
**Office:** Middlesex 103b.
**Office Phone:** 661-2111 x86530.
**Office Hours:** after class.
**Class times and location:** Tuesdays 2 pm to 3:50 pm
and Thursdays 10 am to 11:50 am, MC106.
**Prerequisites:** Group theory and linear algebra,
or permission of instructor.

**Text:** The text is Shlomo Sternberg's
Group Theory in Physics.
The library
copy will be on reserve starting May 1.
I will have the book store order several copies. (But I just heard
that they may not be in for several weeks.)
You can also buy it from
amazon.ca.
You can view some of the introductory pages (including the table
of contents) at
amazon.com.

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

**Evaluation:** Homework will be due roughly every
two weeks. Evaluation will be based upon homework
and the presentations. There will be no tests.

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