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. The idea of the proof is to use the two geometric realizations of the affine Hecke algebra, and relate the Iwahori invariants to Maulik--Okounkov's stable envelopes and Brasselet--Schurmann--Yokura's motivic Chern classes for the Langlands dual group. Joint work with P. Aluffi, L. Mihalcea and J. Schurmann. |