Double Satake diagrams and canonical forms in compact symmetric triads

TL;DR

This paper introduces double Satake diagrams and canonical forms for compact symmetric triads, providing new proofs and establishing existence and properties of canonical forms, advancing the classification theory in this area.

Contribution

It introduces double Satake diagrams and canonical forms for compact symmetric triads, offering alternative proofs and new structural insights.

Findings

Alternative proof of classification theorem for compact symmetric triads

Existence of canonical forms for compact simple symmetric triads

Properties of canonical forms

Abstract

In this paper, we first introduce the notion of double Satake diagrams for compact symmetric triads. In terms of this notion, we give an alternative proof for the classification theorem for compact symmetric triads, which was originally given by Toshihiko Matsuki. Secondly, we introduce the notion of canonical forms for compact symmetric triads, and prove the existence of canonical forms for compact simple symmetric triads. We also give some properties for canonical forms.