Kazhdan-Lusztig polynomials are a big mystery. On a recent work with Leonardo Patimo (following Geordie Williamson) we were able to calculate them explicitly for affine A2. We dream of a similar description for all affine Weyl groups, but it seems like an incredibly difficult program. I will explain some new results in this direction and what we believe that is doable. Another part of this project is to produce an approach towards the following question: for a given element in an affine Weyl group, what are the prime numbers p such that the p-canonical basis is different from the canonical basis?
This is a joint project with Leonardo Patimo and David Plaza.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
