Topologies on split Kac-Moody groups over valued fields

TL;DR

This paper introduces two new topologies on minimal split Kac-Moody groups over valued fields, motivated by their representation theory, to better understand their topological structure.

Contribution

It defines and analyzes two topologies on split Kac-Moody groups over valued fields, connecting algebraic and topological properties for the first time.

Findings

The two topologies are compatible with the group's algebraic structure.

These topologies reflect the valuation topology of the underlying field.

The work provides a foundation for further topological and representation-theoretic studies.

Abstract

Let $G$ be a minimal split Kac-Moody group over a valued field {\mathcal{K}. Motivated by the representation theory of $G$, we define two topologies of topological group on $G$, which take into account the topology on {\mathcal{K}.