EKOR strata and Bruhat-Tits strata for unramified GU(1,n-1) Rapoport-Zink spaces

Speaker: Dr. Joseph Muller，National Taiwan University

Title: EKOR strata and Bruhat-Tits strata for unramified GU(1,n-1) Rapoport-Zink spaces

Language: English  

Time & Venue: 2026.07.15   16:30-17:30   MCM110

Abstract: A certain family of basic affine Deligne-Lusztig varieties (ADLV) admit a natural decomposition, up to perfection, into a disjoint union of classical Deligne-Lusztig (DL) varieties. This is usually referred to as the (weak) Bruhat-Tits (BT) stratification. More precisely, the ADLVs decompose into EKOR strata, and each EKOR stratum is a disjoint union of copies of a DL variety. In such cases, the corresponding local datum is said to be fully Hodge-Newton decomposable, and Görtz, He and Nie have classified all such local data.

ADLVs can be viewed as group-theoretic incarnations of the special fibers of Rapoport-Zink spaces, and govern much of their geometry. On the geometric side, BT stratifications have been constructed on a case by case basis, and often at maximal parahoric level. Recently, we constructed the BT stratification for the unramified GU(1,n−1) Rapoport–Zink space at arbitrary parahoric level. In this talk, I will explain how this stratification relates to the geometric EKOR stratification, and describe the combinatorics underlying their comparison.