Math 9140L: Representation Theory, Summer 2022

(Course outline version: April 10, 2022; may be updated later.)

Instructor Info:

Nicole Lemire,, MC 103C.

Lecture Info:

MW 10:00am-12:00pm, MC 108.


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. 


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 : (35%), 5-6 assignments, roughly equally distributed during the term. 

Presentation : (25%)50 minute presentation and written report

Final Exam: (40%)

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.; showing your work to other students; uploading questions or solutions to a web site; and accessing a web site used for providing solutions (even if you do not use any solutions on the site). The penalty for an academic offence involving a final exam will be a failing grade in the course. The penalty for each academic offence involving homework will be a grade of 0 on the homework set as well as a penalty of negative 5% on the overall course grade. In some cases, the penalty can include expulsion from the program. All academic offences 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. Details and potential list of topics will be posted on OWL.


Attendance: Our class is small and someone's absence can greatly impact the rest of the class. Therefore you are expected to attend class or to let me know in advance when you are unable to attend.

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:



Online access required:  We will be using GradeScope for homework and exams. By taking this course, you are consenting to the use of this software. Completion of this course will require you to have a laptop or computer, a reliable internet connection, a working microphone, a working webcam, and a device for scanning (either a scanner or an app that can be used in conjunction with your device's camera).



UWO e-mail:  The centrally administered e-mail account provided to students will be considered the individual's official university e-mail address. It is the responsibility of the account holder to ensure that e-mail received from the University at his/her official university address is attended to in a timely manner.

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 sites: and

Medical Accommodation:

A student requiring academic accommodation due to illness should bring a Student Medical Certificate with them when visiting an off-campus medical facility and use a Record Release Form for visits to Student Health Services.

If homework is missed and sufficient documentation is provided, the homework can be handed in later.

Failure to follow these rules may result in a grade of zero.

Support Services: Learning-skills counsellors at the Student Development Centre are ready to help you improve your learning skills. Students who are in emotional/mental distress should refer to Mental Health@Western for a complete list of options about how to obtain help. Additional student-run support services are offered by the USC. The website for Registrarial Services is

Student Accessibility Services: Please contact the course instructor if you require material in an alternate format or if you require any other arrangements to make this course more accessible to you. You may also wish to contact Student Accessibility Services (formerly Services for Students with Disabilities, SSD) at 519-661-2111 x82147 for any specific question regarding an accommodation.

Western is committed to achieving barrier-free accessibility for all its members, including graduate students. As part of this commitment, Western provides a variety of services devoted to promoting, advocating, and accommodating persons with disabilities in their respective graduate program.

Graduate students with disabilities (for example, chronic illnesses, mental health conditions, mobility impairments) are encouraged to register with Student Accessibility Services, a confidential service designed to support graduate and undergraduate students through their academic program. With the appropriate documentation, the student will work with both SAS and their graduate programs (normally their Graduate Chair and/or Course instructor) to ensure that appropriate academic accommodations to program requirements are arranged. These accommodations include individual counselling, alternative formatted literature, accessible campus transportation, learning strategy instruction, writing exams and assistive technology instruction.


In the event of a COVID-19 resurgence during the course that necessitates the course delivery moving away from face-to-face interaction, all remaining course content will be delivered entirely online, either synchronously (i.e., at the times indicated in the timetable) or asynchronously (e.g., posted on OWL for students to view at their convenience). The grading scheme will not change. Any remaining assessments will also be conducted online as determined by the course instructor.

In the event of a health lockdown, tests and examinations in this course will be conducted using a remote proctoring service. By taking this course, you are consenting to the use of this software and acknowledge that you will be required to provide personal information (including some biometric data) and the session will be recorded. Completion of this course will require you to have a reliable internet connection and a device that meets the technical requirements for this service. More information about this remote proctoring service, including technical requirements, is available on Western’s Remote Proctoring website at: