Totally geodesic submanifolds and root subsystems

03 Mai 2024
Aula 10 da Facultade de Matemáticas, USC

"Totally geodesic submanifolds and root subsystems", organizado polo CITMAga. Será impartido por Ivan Solonenko (Universität Stuttgart, Alemaña).

Data: Venres 3 de maio de 2024.

Hora: 16:00 h.

Lugar: Aula 10 da Facultade de Matemáticas, USC.


In this talk, I will present some structure results on totally geodesic submanifolds in symmetric spaces and relate them to the theory of root systems and their subsystems. As an application, we will see how this allows to largely reduce classification of totally geodesic submanifolds of full rank to that of (generalized) maximal root subsystems. Even though a classification of closed root subsystems is known (and follows, for instance, from Borel-de Siebenthal theory), certain root systems also admit nonclosed (maximal) root subsystems. Those are essentially of no use within the framework of complex semisimple Lie algebras and thus have been largely disregarded. Yet, when one switches to real Lie algebras, such subsystems play an important role. If time allows, we will also discuss complex totally geodesic submanifolds in Hermitian symmetric spaces (initially classified by Satake and Ihara) and present an alternative approach to their classification.