Stability phenomena for Kac-Moody groups

TL;DR

This paper demonstrates that extending generalized Dynkin diagrams produces Kac-Moody groups with homological stability and explores emergent structures during stabilization, with applications to string theory.

Contribution

It introduces a canonical extension procedure for Dynkin diagrams that ensures homological stability in Kac-Moody groups, revealing new structural insights.

Findings

Families of Kac-Moody groups exhibit homological stability.

Homotopy decompositions are effective in analyzing classifying spaces.

Emergent structures appear on stabilization of these groups.

Abstract

We show that a canonical procedure of extending generalized Dynkin diagrams gives rise to families of Kac-Moody groups that satisfy homological stability. We also briefly sketch some emergent structure that appears on stabilization. Our results are illustrated for the family {E_n} which is of interest in String theory. The techniques used involve homotopy decompositions of classifying spaces of Kac-Moody groups.