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# Math 9140L Summer 2020: Representation Theory

### Instructor Info:

Nicole Lemire, nlemire@uwo.ca, MC 103C.

### Lecture Info:

MWF 10:00-11:15am; offered online. Notes will be posted. A combination of recorded lectures and Zoom lectures will be used to present the material. The lecture time may also be used for office hours and testing using Zoom. The exact composition will be determined as the class progresses according to student preferences.

### Textbook:

*Representation Theory of Finite Groups: An Introductory Approach, by Benjamin Steinberg, 2012, Springer.*Via the library proxy, this book can be downloaded for free.

### Additional references:

J.P. Serre,* Linear Representations of Finite Groups, *GTM 42, Springer, 1977

W. Fulton and J. Harris, Representation theory, GTM 129, Springer 1991.

### Prerequisite:

Group Theory, Linear Algebra

### Course Description:

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. Other possible topics include representations of the symmetric groups (partitions, Young tableaux, Young symmetrizers, Specht modules, etc), Brauer and Artin Theorems, Clifford theory.

### Evaluation of Student Performance:

**Assignments :**

**(40%),**6 assignments, roughly one every 1.5 weeks.

**Testing :** 60 (%)*. Combination of Video-supervised written tests/exams, oral examination, presentation and written report.*

**Assignments:** Assignments 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:** Each student will give a presentation and prepare a written report on a topic related to the course.

**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