A remark on the Kottwitz homomorphism

TL;DR

This paper proves the existence of a homomorphic section for the Kottwitz homomorphism in split almost-simple reductive groups over p-adic fields, extending the result to some additional groups.

Contribution

It establishes the existence of a homomorphic section for the Kottwitz homomorphism in specific classes of reductive groups over p-adic fields, which was previously unknown.

Findings

Existence of a homomorphic section for the Kottwitz homomorphism in split almost-simple groups.

Extension of the result to certain additional split connected reductive groups.

Provides a new structural insight into the Kottwitz homomorphism.

Abstract

We prove that for any split almost-simple connected reductive group G over a p-adic field F, the Kottwitz homomorphism exhibits a homomorphic section. We then extend this result to certain additional split connected reductive groups.