Special Year 2020-21: Geometric and Modular Representation Theory

Covers chapter 8 in Jantzen's book.

The anti-spherical modules over the affine Hecke algebras admit two different realizations: one realization is in terms of the space of Whittaker functions on the affine flag manifolds and the other realization, due to Kazhdan-Lusztig, is in terms...

Continuation of the talk from last time.

We will discuss the following theorems concerning colimits taken in the infinity-category of monoidal DG-categories. (No familiarity with infinity-categories will be required or assumed.) The affine Hecke category is the monoidal colimit of its...

In this talk we will present two perspectives on the p-Kazhdan-Lusztig basis and its combinatorics, giving a glimpse of its complexity. This talk does not provide many answers, but will hopefully raise many interesting questions and is based on...

A theorem of Bernstein identifies the center of the affine Hecke algebra of a reductive group $G$ with the Grothendieck ring of the tensor category of representations of the dual group $G^\vee$. Gaitsgory constructed a functor which categrorifies...

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.