Math 445 – Representation Theory, Winter 2026

University of Toronto

Syllabus

Syllabus (PDF)

Instructor

Name: Daniel Litt

Email: daniel.litt@utoronto.ca

Office Hours: 10am Wednesdays, Huron 1018

Teaching Assistant

Name: Alexander Mirabella

Email: alexander.mirabella@mail.utoronto.ca

Textbooks / Course Readings

Notes from last year, taken by Cole Franklin and Yun-chi Tang

See here: Notes

Mark Breakdown

Component Percentage
Assignments (best 4 of 5) 40%
Term Test 25%
Final Assessment 35%

Assignments

There will be 5 assignments. The assignment with the lowest grade will be dropped. Late submissions receive a mark of zero unless an extension is granted by the instructor. Tentative due dates are listed in the lecture schedule below.

Term Test

There will be one term test, which is 2 hours long, on February 26 in class.

Final Assessment

The final assessment will be held during the final assessment period in April 2026, scheduled by the registrar.

Schedule of Lectures

Week Dates Topics
Week 1 Jan 5 - Jan 9 Basics of representation theory of groups, semisimplicity, beginnings of character theory
Week 2 Jan 12 - Jan 16 Character theory, examples, induction and restriction, tensor products, HW 1 due
Week 3 Jan 19 - Jan 23 Group algebra, field of definition, Brauer’s theorem, examples
Week 4 Jan 26 - Jan 30 Symmetric groups, HW 2 due
Week 5 Feb 2 - Feb 6 SL2(Fp)
Week 6 Feb 9 - Feb 13 Lie algebras, sl2, HW 3 due
Week 7 Feb 16 - Feb 20 Reading week (no classes)
Week 8 Feb 23 - Feb 27 sl2 continued, and an application to combinatorics, Term Test (Feb 26)
Week 9 Mar 2 - Mar 6 More Lie algebras, ideals, semisimplicity, Killing form, HW 4 due
Week 10 Mar 9 - Mar 13 Complete reducibility
Week 11 Mar 16 - Mar 20 Representations of semisimple Lie algebras
Week 12 Mar 23 - Mar 27 Classification of semisimple Lie algebras
Week 13 Mar 30 - Apr 3 Classification continued, HW 5 due