Representation Theory, Math 9140L, Summer 2018

• Instructor: Dan Christensen
• E-mail: [email protected]
• Office: Middlesex 103b. Office hours after class.
• Class times and location: TuTh 10:00-11:45, May 1 to July 5, MC107.
• Prerequisites: Group theory and linear algebra.

Outline:

This course will study the representation theory of finite groups as well as some applications: irreducibility, complete reducibility, Schur's lemma, character theory, induced representations, Fourier analysis on finite groups, applications to group theory, including theorems of Burnside, etc. Other possible topics include representations of the symmetric groups (partitions, Young tableaux, Young symmetrizers, Specht modules, etc) and 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 Thursday, July 12, from 9-noon.

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/pdf/academic_policies/appeals/scholastic_discipline_grad.pdf