Abstract :

In many contexts of Lie theory, the classification of all closed subroot systems of a given root system becomes a fundamental issue. For instance, it is important to classify all closed subroot systems of a given root system in order to address the following problems: (1) the classification of closed connected subgroups of a compact Lie group that have maximal rank (Bore-de Siebenthal theory, 1949) (2) the classification of semi-simple subalgebras of a given finite-dimensional semi-simple Lie algebra (Dynkin, 1950) (3) the classification of reflection subgroups of corresponding Weyl groups (Dyer-Lehrer, 2011) The classification of closed subroot systems problem can be easily reduced to the classification maximal closed subroot systems problem. In this talk, I will explain you how to get this classification in the case affine root systems. This is joint work with Krishanu Roy. No knowledge of root systems will be assumed in this talk.