Stability phenomena for Kac-Moody 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.

The original version is expanded to identify the stable cohomology ring with the stable Weyl invariants up to a nilpotent extension