Changjian Su, University of Toronto – Geometric Methods in Representation Theory Seminar

Title: Motivic Chern classes, K-theoretic stable basis and Iwahori invariants of principal series

Abstract: Let G be a split reductive p-adic group. In the Iwahori-invariants of an unramified principal series representation of G, there are two bases, one of which is the so-called Casselman basis. In this talk, we will prove a conjecture of Bump–Nakasuji–Naruse about certain transition matrix between these two bases. We will first relate the Iwahori invariants to Maulik–Okounkov’s stable envelopes and Brasselet–Schurmann–Yokura’s motivic Chern classes for the Langlands dual groups. Then the conjecture follows from a K-theoretic generalization of Kumar’s smoothness criterion for the Schubert varieties. This is based on joint work with P. Aluffi, L. Mihalcea and J. Schurmann.