A duality between non-compact semisimple symmetric pairs and commutative compact semisimple symmetric triads and its general theory

Kurando Baba, Osamu Ikawa, Atsumu Sasaki

Research output: Contribution to journalArticlepeer-review

Abstract

The present paper investigates a natural generalization of the duality between Riemannian symmetric pairs of compact type and those of non-compact type à la É. Cartan. The main result of this paper is to construct an explicit description of a one-to-one correspondence between non-compact pseudo-Riemannian semisimple symmetric pairs and commutative compact semisimple symmetric triads, which is called the duality theorem. Further, we develop a general theory of the duality theorem.

Original languageEnglish
Article number101751
JournalDifferential Geometry and its Application
Volume76
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Commutative compact symmetric triad
  • Duality theorem
  • Involution
  • Irreducibility
  • Non-compact symmetric pair
  • Type K symmetric pair

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