Tuesday, April 21 2020
12:00 - 13:30

#### The classification of closed subroot systems of finite root systems was crucial in the classification of semi-simple subalgebras of simple Lie algebras. In this talk, We will completely classify and give explicit descriptions of the maximal closed subroot systems of affine root systems. Dynkin showed that linearly independent \pi systems arise precisely as a simple system of closed subroot systems. He also computed the number of Weyl group orbits for each \pi-system in finite root systems. We compute the number of Weyl group orbits for certain \pi-systems in simply-laced Kac-Moody algebras.

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