Iwasawa decompositions of split Kac-Moody groups

TL;DR

This paper characterizes fields over which certain split Kac-Moody groups and algebraic groups admit an Iwasawa decomposition, extending classical results to a broader class of infinite-dimensional groups.

Contribution

It provides a complete characterization of fields allowing Iwasawa decompositions for split Kac-Moody groups, generalizing known results for algebraic groups.

Findings

Identifies all fields F where split Kac-Moody groups have Iwasawa decompositions

Includes split semisimple algebraic groups as special cases

Extends classical Iwasawa decomposition theory to Kac-Moody groups

Abstract

We characterize all fields F for which a group with an F-locally split root group datum admits an Iwasawa decomposition. This class of groups in particular includes the split semisimple algebraic groups and the split Kac-Moody groups.