# Representation Theory, Math 9140L, Summer 2016

This course will study the representation theory of finite groups as well as some applications. Basic background in group theory and linear algebra will be assumed.
• Instructor: Dan Christensen
• E-mail: jdc@uwo.ca
• Office: Middlesex 103b.
• Office Phone: 661-2111 x86530.
• Office Hours: Wednesdays after class (Monday/Friday too, if quick)
• Class times and location: MWF 10:00-11:10, MC108, May 2 to July 15, except May 16-20 and June 20-24.
• Prerequisites: Group theory and linear algebra.

## Outline:

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

Possible further topics include:

• Fourier analysis on finite groups
• Applications to group theory, including theorems of Burnside.
• Representations of the symmetric groups: partitions, Young tableaux, Young symmetrizers, Specht modules, and lots more.
• Probability and random walks on graphs.

Text: The text is Representation Theory of Finite Groups: An Introductory Approach, by Benjamin Steinberg, 2012, Springer. From on campus, you should be able to download it for free via this link.

Other references you may find useful, but which are not required:

• J.P. Serre, Linear Representations of Finite Groups, GTM 42, Springer, 1977.
• A. Baker, Representations of Finite Groups, pdf notes.
• Shlomo Sternberg, Group theory in physics. A pleasant book with a conversational style and lots of applications to motivate the material.
• W. Fulton and J. Harris, Representation theory, GTM 129, Springer, 1991. Starts with a very fast treatment of the representation theory of finite groups.

Homework: Homework will be due roughly every 1.5 weeks. Doing problems and talking about the material are both essential for learning the material in this course, so you are encouraged to discuss the problems with classmates and with me. But you must write up the solutions on your own and must not look at other students' written solutions nor should you attempt to find solutions to problems online or in textbooks. Your solutions should be clear and carefully written and you should give credit to those who helped you and to any references you used. Homework will be graded based on both correctness and clarity. Late problem sets will not be accepted unless arranged in advance for a good reason.

Copying solutions from other students, online sources, textbooks, etc., or showing your work to other students constitutes a scholastic offense and will result in a grade of negative 100% for the assignment and in some cases expulsion from the program. All academic offenses are added to your student record.

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

Exam: The final exam will be on Monday, July 25, from 1 to 4pm, in MC107.

Evaluation: Evaluation will be based upon homework, presentations and the final exam, with equal weight.

Scholastic offences:  Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at the following Web site: http://www.uwo.ca/univsec/handbook/appeals/scholastic_discipline_grad.pdf