Root subsystems of loop extensions

TL;DR

This paper classifies all real root subsystems of loop algebra root systems, introducing new concepts like admissible subgroups and scaling functions, thereby generalizing previous affine root system results.

Contribution

It provides a complete classification of root subsystems for loop algebra root systems using novel notions of admissible subgroups and scaling functions.

Findings

Complete classification of real root subsystems

Introduction of admissible subgroups and scaling functions

Generalization of earlier affine root system work

Abstract

We completely classify the real root subsystems of root systems of loop algebras of Kac-Moody Lie algebras. This classification involves new notions of "admissible subgroups" of the coweight lattice of a root system $\Psi$, and "scaling functions" on $\Psi$. Our results generalise and simplify earlier work on subsystems of real affine root systems.