Central leaves in loop groups

TL;DR

This paper investigates the detailed structure of Newton strata in loop groups, focusing on the definition, geometric properties, and closure behavior of central leaves within these strata.

Contribution

It introduces the concept of central leaves in loop groups and determines their global geometric structure, advancing understanding of their role in the stratification.

Findings

Central leaves are well-defined within Newton strata.

The global geometric structure of central leaves is characterized.

Properties of the closure of central leaves are established.

Abstract

This paper analyses the finer structure of Newton strata in loop groups. These can be decomposed into so-called central leaves. We define them, and determine their global geometric structure. We then study the closure of central leaves, both by proving some general properties and by considering an illustrative example.