Generic Newton points and cordial elements

TL;DR

This paper characterizes generic $\sigma$-conjugacy classes within the Iwahori-Bruhat decomposition of reductive groups and uses this to classify cordial elements, advancing understanding of their structure.

Contribution

It introduces a description of generic $\sigma$-conjugacy classes and provides a classification of cordial elements, linking these concepts in the context of reductive groups.

Findings

Classification of cordial elements

Description of generic $\sigma$-conjugacy classes

Connection between conjugacy classes and cordial elements

Abstract

We describe the generic $\sigma$-conjugacy classes associated with the Iwahori-Bruhat decomposition of a reductive group. As an application, we classify cordial elements as introduced by Mili\'cevi\'c-Viehmann.