Australian Category Seminar

Category $\mathcal{O}$ is an important subcategory of representations of a Lie algebra. It contains all finite dimensional modules and Verma modules. A natural question first posed by Verma was to determine the Jordan–Holder multiplicities of Verma modules. This turns out to be an extremely subtle question whose answer was given using the Kazhdan–Lusztig theory of the Lie algebra’s Weyl group. In this talk, I’ll introduce Category $\mathcal{O}$ and explain how its generalisation have been used to resolve many long-standing questions in Kazhdan–Lusztig theory.

This talk should be accessible to a broad audience. No prior knowledge of Category $\mathcal{O}$ will be required.