Representation theory: 797RT

The class meets on MoWe 8:40AM - 9:55AM
LGT 1334
My office: 1238 LGRT
Office Hours: Mo, We 2:30PM-3:30PM or by appointment
Course webpage:


We are planning to cover basics of representation theory as well as key methods. The key examples that are covered in class are finite groups, $GL_n(\mathbb{C})$, $S_n$, $GL_2$ over finite field and quiver algebras. If time permits, we cover theory of Soergel bimodules and applications to knot homology.

Main Textbook

Introduction to Representation Theory, by Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner
It is available online:

Other books and further reading

Representations of $SL_2(F_q)$, by Cedric Bonnafe
Quiver Representations and Quiver Varieties, by Alexander Krillov Jr.
$SL_2(R)$, by Serge Lang.
Introduction to Soergel bimodules, by Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson.



Homework will be assigned bi-weekly. We will have group solving sessions in class for the problem sets. A convenient time for homework meeting will be discussed in class.


Grade is assigned based on homework: 60%, Final presentation: 30% and class discussion participation 10%.

Presentation topics

1.Representation theory of SL(2,F_q), Drinfeld curve. Source: Bonnafe, Representation theory of SL_2(F_q)

2. BMW algebras. Source: Survey by Geordie Williamson available at

3. Quantum groups: U_q(sl_2) and R-matrices. Source: Cassel, Quantum groups

4. Compact Lie groups and Lie algebras exponential map. Source: Hall, Lie groups, Lie algebras and representations: an elementary intrduction

5. Lie algebra of type G_2, roots and representation theory. Source: Humphreys, Introduction to Lie Algebras and Representation theory

6. Lattices, E_8, classification of indefinite lattices. Source: Serre, Course of arithmetics.

7. Inductive approach to representatio theory of S_n. Source: Okounkov, Vershik

8. Homology of Lie algebras, central extensions. Source: Weibel, An introduction to homological algebra.

9. Temperley-Lieb algebras, graphical calculus and Jones-Wentzel projectors. Source: Khovanov's thesis,