#### Alladi Ramakrishnan Hall

#### Thesis defense: pi-systems of Kac-Moody Lie algebras

#### Krishanu Roy (Zoom 872 2731 4427)

##### IMSc

*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.

Done