This course will study the representation theory of finite groups as well as some applications. Main topics: 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:
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.
Presentations: In the second half of the semester, each student will give a 50 minute presentation on a topic related to the course. Here is a list of potential topics.
Exam: The final exam will be a three hour exam on Friday, July 12 from 2-5pm in MC107.
Evaluation: Evaluation will be based upon homework, presentations and the final exam, with equal weight.
UWO e-mail: In accordance with this policy, 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 site: https://www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_grad.pdf
Scholastic offences include: Copying solutions from other students, online sources, textbooks, etc.; showing your work to other students; using a large language model or any other source to help with solutions; 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 the 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. The penalty for an academic offence involving the presentation will be a grade of 0 on the presentation. In some cases, the penalty can include expulsion from the program. All academic offences are added to your student record.
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 up to three days late, or can be reweighted to the other homework sets, depending on the period covered by the documentation.
If the presentation is missed, it will be delayed, or if that it not possible, it will be reweighted to the final exam.
If an exam is missed and sufficient documentation is provided, a make-up exam will be offered.
Failure to follow these rules may result in a grade of zero.
Support Services: Learning-skills counsellors at Learning Development & Success are ready to help you improve your learning skills. Students who are in emotional/mental distress should refer to Mental Health at 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 https://www.registrar.uwo.ca.
Student Accessibility Services: Please contact the course instructor if you require lecture or printed material in an alternate format or if any other arrangements can make this course more accessible to you. You may also wish to contact Accessible Education at http://academicsupport.uwo.ca/accessible_education/index.html if you have any questions regarding accommodations.
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.
Western is committed to reducing incidents of gender-based and sexual violence and providing compassionate support to anyone who has gone through these traumatic events. If you have experienced sexual or gender-based violence (either recently or in the past), you will find information about support services for survivors, including emergency contacts at this link. To connect with a case manager or set up an appointment, please contact [email protected].
Additional student-run support services are offered by the USC.
If students need assistance with the course OWL Brightspace site, they can seek support on the OWL Brightspace Help page. Alternatively, they can contact the Western Technology Services Helpdesk. The Helpdesk can also be contacted by phone at 519-661-3800 or ext. 83800.