Motivic Chern classes and Iwahori invariants of principal series

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. The ingredients of the proof include Maulik–Okounkov’s stable envelopes and Brasselet–Schurmann–Yokura’s motivic Chern classes for the Langlands dual groups. This is based on joint work with P. Aluffi, L. Mihalcea and J. Schurmann.