MAT445H1: Representation Theory

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

Serre, Linear Representations of Finite Groups
Kirllov, Introduction to Lie Groups and Lie Algebras
Okounkov, Vershik, A new approach to representation theory of symmetric groups
Fulton and Harris, Representation Theory: A First Course

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	$\mathrm{SL}_2(\mathbf F_p)$
Week 6	Feb 9 - Feb 13	Lie algebras, $\mathfrak{sl}_2$, HW 3 due
Week 7	Feb 16 - Feb 20	Reading week (no classes)
Week 8	Feb 23 - Feb 27	$\mathfrak{sl}_2$ 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