# Representation Theory, Math 9140b, Winter 2010

This course will study the representation theory of finite groups
and Lie groups, with a focus on the symmetric groups and linear
groups, and the relationships between these two.
Basic background in group theory, modules and linear algebra
will be assumed.
**Instructor:** Dan Christensen
**E-mail:** jdc@uwo.ca
**Office:** Middlesex 103b.
**Office Phone:** 519-661-2111 x86530.
**Office Hours:** after class or by appointment.
**Class times and location:** Mondays and Wednesdays,
10:00 to 11:30, MC108. **Starts Jan 6.**
**Prerequisites:** Group theory, modules and linear algebra.

## Outline:

Basic representation theory: irreducibility, complete reducibility,
Schur's lemma, character theory, induced representations, etc.

Representations of the symmetric groups: partitions, Young tableaux,
Young symmetrizers, Specht modules, and lots more.

Representations of the special and general linear groups:
polynomial and rational representations, complete reducibility,
characters, tensor representations, and lots more.

**Text:** There is no text for the course. Some
references you may like to use:

- W. Fulton,
*Young tableaux*, LMSST 35, Cambridge Univ. Press, 1997.
- G.D. James and A. Kerber,
*The representation theory of the symmetric
group*, Addison-Wesley or Cambridge Univ. Press, 1981. 532pp.
- Shlomo Sternberg,
*Group theory in physics*. A pleasant book
with a conversational style and lots of applications to motivate the
material.
- G.D. James,
*The representation theory of the symmetric
groups*, Lecture Notes in Math., Vol. 682, 1978. 161pp.
- W. Fulton and J. Harris,
*Representation theory*, GTM 129, Springer, 1991.
- And there are lots more!

**Homework:** Homework will be due roughly every two weeks.
I encourage discussion of the class material with other students, and
I encourage you to consult textbooks to learn more. But don't copy
solutions from students or texts, and when a student or a text helps
you solve a problem, you should give credit.

**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 (40%),
presentations (30%) and the final exam (30%).

Back to Dan Christensen's home page.

Western Mathematics Home Page