Representation Theory of Finite Groups, Math 691
|Professor: Dr. Cathy Kriloff
|Office/Phone: PS 316C / 282-3093
|Math Dept. Phone: 282-3350
||Web Page: www.isu.edu/~krilcath
|Math Dept. Fax: 282-2636
Office Hours: Monday
Wednesday and Friday 10:00-11:00am, but feel free to stop by at other
times, send e-mail, or make an appointment.
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
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
- Have given a presentation on one or more specific topics related
to representation theory of finite groups.
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.
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.
be assigned and collected periodically. Studying
discussing problems are encouraged, after
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.
will be assigned based on homework (70%) and in-class presentation
Our program is committed to all students achieving their
you have a disability or
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.