Speaker：Si'an Nie(Chinese Academy of Sciences)

Time：2022-06-24, 15:00

Location：Tencent Meeting ID：436-5742-3564（No Password）

Abstract:

Affine Deligne-Lusztig varieties play an important role in the theory of Shimura varieties. Their geometries are controlled by the Newton strata in Iwahori double cosets. In this talk, I will report a multiplicity-one phenomenon on the Newton strata of a large class of Iwahori double cosets, namely, these strata form a stratification and each of them is nonempty and irreducible. We prove it by counting rational points on the Newton strata. As a consequence, we show the corresponding affine Deligne-Lusztig varieties are explicit unions of classical Deligne-Lusztig varieties of Coxeter type. This is based on joint work in progress with X. He and Q. Yu.