On a "Wonderful" Bruhat-Tits group scheme

TL;DR

This paper constructs Bruhat-Tits group schemes on wonderful embeddings for various groups, providing a universal framework that captures their orbit structures in both absolute and relative contexts.

Contribution

It introduces a universal construction of Bruhat-Tits group schemes on wonderful embeddings for adjoint groups and Kac-Moody groups, highlighting their classifying properties.

Findings

Provides a universal construction of Bruhat-Tits group schemes

Characterizes orbit structures on wonderful embeddings

Extends constructions to Kac-Moody groups

Abstract

In this note we make a universal construction of Bruhat-Tits group scheme on wonderful embeddings of adjoint groups in the absolute and relative settings and of adjoint Kac-Moody groups. These have natural classifying properties reflecting the orbit structure on the wonderful embeddings.