University of Toronto
Name: Daniel Litt
Email: daniel.litt@utoronto.ca
Office Hours: 10am Wednesdays, Huron 1018
Name: Alexander Mirabella
See here: Notes
| Component | Percentage |
|---|---|
| Assignments (best 4 of 5) | 40% |
| Term Test | 25% |
| Final Assessment | 35% |
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.
There will be one term test, which is 2 hours long, on February 26 in class.
The final assessment will be held during the final assessment period in April 2026, scheduled by the registrar.
| 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 |