Special Year 2020-21: Geometric and Modular Representation Theory - Seminar

In this talk, we will put together all ingredients we have seen in the last couple of talks to describe the algorithm to calculate tilting characters for reductive algebraic groups in the anti-spherical module. We will try to illustrate the most...

Continuation of the talk from Feb 4.

This is the second in a series of talks on "two realizations." We discuss equivariantization and de-equivariantization for a group $G$, which relate categories with $G$-actions and categories with RepG-actions, and how this relates to the notion of...

Last week, Ben explained how diagrammatic algebra helps understand tilting characters. In Ben's talk the diagrammatic algebra was that of Temperley-Lieb flavour and its higher rank cousins (webs etc.) I will briefly recall the diagrammatics for the...

The talk covers Chapter 6 in Jantzen's book.

In the upcoming series of talks we discuss some equivalences by Bezrukavnikov between categories of coherent sheaves on Steinberg varieties and of perverse sheaves on the affine flag variety. In this talk I discuss the decategorified isomorphism...

A basic technique in algebra, when describing a difficult-to-approach category like Tilt, is to choose a projective generator and study its endomorphism ring. The modern twist on this technique is to choose the projective generator with great...

Continuation of the talk from last time.

Wall-crossing functors on the principal block of category $O$ give an action of the (finite) Hecke category. If one knows enough about the Hecke category, one can deduce the Kazhdan-Lusztig conjectures from the existence of this action. This is a...

I will explain the basics of tilting modules for reductive algebraic groups and why we should care about their characters. In particular, I will discuss Donkin's tensor product theorem and the relation to modular representations of symmetric groups...