Invariant measures for unitary forms of Kac-Moody groups, Parts I-III

TL;DR

This paper investigates invariant measures on formal completions of Kac-Moody groups, establishing existence in affine cases and discussing conjectures and uniqueness properties for these measures.

Contribution

It provides new results on the existence and conjectures regarding the uniqueness of invariant measures for Kac-Moody groups and their homogeneous spaces.

Findings

Existence of invariant measures proven for all affine types.

Formulated conjectures on the uniqueness of these measures.

Analyzed properties of formal completions of Kac-Moody groups.

Abstract

The purpose of this paper is to describe some conjectures and results on the existence and uniqueness of invariant measures on formal completions of Kac-Moody groups and associated homogeneous spaces. Existence is rigorously established in all affine type cases.