October 2: Nicolas Libedinsky (Universidad de Chile)

On Kazhdan-Lusztig theory for affine Weyl groups

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.

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