Course Information-Math 691, Spring 2005

Course Information
Representation Theory of Finite Groups, Math 691
Spring, 2005

Professor: Dr. Cathy Kriloff	Office/Phone: PS 316C / 282-3093	Math Dept. Phone: 282-3350
E-mail: krilcath@isu.edu	Web Page: www.isu.edu/~krilcath	Math Dept. Fax: 282-2636

Office Hours: Monday 12:00pm-1:00pm, Tuesday 11:00am-12:00pm, Wednesday and Friday 10:00-11:00am, but feel free to stop by at other times, send e-mail, or make an appointment.

Objectives: Representation theory is a way of analyzing abstractly defined objects by realizing them concretely as matrices acting on vector spaces. The study of properties of these matrices (such as traces and eigenspaces) then provides information about the structure of the algebraic object, combining aspects of both linear algebra and abstract algebra. The foundations of representations of finite groups go back to the work of Frobenius and Schur at the turn of the twentieth century. Many aspects of representation theory of a variety of algebraic objects are being worked out in current research.

By the end of this course you will:

Know and be able to use the foundational results in the representation theory of finite groups.
Understand and be able to construct the character table of several important examples of groups.
Know of applications of representation theory in chemistry and physics.
Have given a presentation on one or more specific topics related to representation theory of finite groups.

Materials: The text is Linear Representations of Finite Groups, by J. P. Serre. Other useful references include:

Representations and Characters of Groups, by G. James and M. Liebeck;
Representation Theory: A First Course, by W. Fulton and J. Harris;
Introduction to Group Characters, by W. Ledermann;
Representation Theory of Finite Groups, by M. Burrow;
Character Theory of Finite Groups, by M. Isaacs.

Prerequisites: We will be using abstract algebra at the level of Math 631 (groups, modules, and tensor products) and some linear algebra. If needed, we will review algebra concepts being used.

Homework will be assigned and collected periodically. Studying together and discussing problems are encouraged, after you have worked hard on the material or problem yourself, since this can be a very effective and rewarding way to learn mathematics. Submitted solutions must be written up independently. If credit is due to another student or reference, give it.

Presentation topics will be suggested during the semester. You will be expected to choose or find a topic, consult at least a few sources on the topic, and prepare an effective class lecture or presentation on the topic. I will be happy to provide some input during both the choice of an appropriate topic and preparation of your presentation.

Grades will be assigned based on homework (70%) and in-class presentation scores (30%).

Accommodations: Our program is committed to all students achieving their potential. If you have a disability or think you have a disability (physical, learning, hearing, vision, or psychiatric) that may need a reasonable accommodation, please contact the ADA Disabilities & Resource Center, Room 123 Graveley Hall, 282-3599 as soon as possible.