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

Kurando Baba; Osamu Ikawa; Atsumu Sasaki

doi:10.1016/j.difgeo.2021.101751

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arXiv · 2002.00896

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

Kurando Baba·Osamu Ikawa·Atsumu Sasaki

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Abstract

The present paper investigates a natural generalization of the duality between Riemannian symmetric pairs of compact type and those of non-compact type \`a la \'E. 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.

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Kurando Baba, Osamu Ikawa, Atsumu Sasaki. 2020-02-03. A duality between non-compact semisimple symmetric pairs and commutative compact semisimple symmetric triads and its general theory. https://doi.org/10.1016/j.difgeo.2021.101751

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