AG Lie-Gruppen: Atsumu Sasaki

Vortragende: Atsumu Sasaki
Veranstalter: Karl-Hermann Neeb

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

Abstract:
A duality between non-compact semisimple symmetric pairs and commutative compact semisimple symmetric triads.
Abstract: It is a well-known fact that there is a one-to-one correspondence between Riemannian semisimple symmetric pairs of compact type and those of non-compact type. This correspondence is usually called the duality for Riemannian semisimple symmetric pairs. In this talk, I will give a survey of a generalization of the duality to pseudo-Riemannian setting. Namely, we provide an explicit description of a one-to-one correspondence between equivalence classes in non-compact pseudo-Riemannian semisimple symmetric pairs and those in commutative compact semisimple symmetric triads. We call it the duality theorem. If time allows, I will mention the motivation on differential geometry and its application to geometric structures of orbits of the symmetric subgroup actions on (not only Riemannian but also pseudo-Riemannian) symmetric spaces.