Double Satake Diagrams and Canonical Forms in Compact Symmetric Triads

Year 2024, Volume: 17 Issue: 2, 466 - 495, 27.10.2024

Kurando Baba , Osamu Ikawa

https://doi.org/10.36890/iejg.1486767

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.

Keywords

Compact symmetric triad, double Satake diagram, canonical form

Thanks

The second author was partially supported by JSPS KAKENHI Grant Number 22K03285.

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