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.