Twisted root system of a (*)-subgroup

TL;DR

This paper classifies (*)-subgroups of compact Lie groups of adjoint type and introduces a twisted root system to analyze their structure, focusing on Weyl groups, finite root data, and infinite root strips.

Contribution

It provides a comprehensive classification of (*)-subgroups and develops the theory of associated twisted root systems, including properties of Weyl groups and root data.

Findings

Classification of (*)-subgroups in compact Lie groups

Development of twisted root system theory

Analysis of Weyl group structures and root data

Abstract

We classify (*)-subgroups of compact Lie groups of adjoint type, and associate a twisted root system to every (*)-subgroup. We study the structure of twisted root system in several aspects: properties of the small Weyl group W_{small} and its normal subgroups W_{tiny} and W_{f}; properties of finite root datum; structure of strips of infinite roots.