**Day/Time:** Tue 9:00 -- 10:00, Wed 16:15 -- 17:15, Fri 13:00 -- 14:00 (26 Jul. - 24 Oct., 2021)

**Location:** Peter Hall G03 (Evan Williams Theatre). Due to lockdown, we will start on Zoom. See LMS for the link.

**Instructor:** Chenyan Wu

**Contact Information:** chenyan.wu "at" unimelb.edu.au

**Office Hour:** M 13:00--14:00, W 11:00--12:00, 17:15--18:15 (On Discord. No in person consultation for now.)

**Office:** Peter Hall Building 208

**Textbooks:**

- Linear Representations of Finite Groups by Jean-Pierre Serre,
- Introduction to Representation Theory by Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena Yudovina with historical interludes by Slava Gerovitch.

### Prerequisites:

Students should be familiar with concepts of vector spaces, groups and rings.

### Course Description:

Symmetries arise in mathematics as groups and Representation Theory is the study of groups via their actions on vector spaces. It has important applications in many fields: physics, chemistry, economics, biology and others. This subject will provide the basic tools for studying actions on vector spaces. The course will focus on teaching the basics of representation theory via favourite examples: symmetric groups, diagram algebras, matrix groups, reflection groups. In each case the irreducible characters and irreducible modules for the group (or algebra) will be analysed, developing more and more powerful tools as the course proceeds. Examples that will form the core of the material for the course include SL_{2}, cyclic and dihedral groups, diagram algebras: Temperley-Lieb, symmetric group and Hecke algebras, Brauer and BMW algebras, compact Lie groups. Among the tools and motivation that will play a role in the study are characters and character formulas, induction, restriction and tensor products, and connections to statistical mechanics, mathematical physics and geometry.
If time permits, there may be some treatment of loop groups, affine Lie algebras and Dynkin diagrams.

### Assessment:

Grade is based on assignments (50%: Up to 50 pages of written assignments (two assignments worth 25% each, due mid and late in semester) and a written examination (50%, during the exam period). Note: Due to the impact of COVID-19, the form of the assessments may change.