Basic loci of Coxeter type with arbitrary parahoric level

TL;DR

This paper classifies and characterizes the basic loci of Coxeter type in the reduction of Shimura varieties using group-theoretic models, providing a comprehensive understanding of their structure and relation to Rapoport-Zink spaces.

Contribution

It offers a complete classification of Coxeter type cases, characterizes them by dimension, and connects these models to Shimura varieties and Rapoport-Zink spaces.

Findings

Complete classification of Coxeter type cases

Dimension-based characterization of basic loci

Discussion of open and known cases in Shimura varieties

Abstract

Motivated by the desire to understand the geometry of the basic loci in the reduction of Shimura varieties, we study their "group-theoretic models" -- generalized affine Deligne-Lusztig varieties -- in cases where they have a particularly nice description. Continuing the work of [GH] and [GHN] we single out the class of cases of Coxeter type, give a characterization in terms of the dimension, and obtain a complete classification. We also discuss known, new and open cases from the point of view of Shimura varieties/Rapoport-Zink spaces.