Title : Bases, Braids, and Beyond

Abstract :

Chevalley's basis for simple Lie algebras has been the preferred basis choice for over a century, and it has given much insight into the structure and representations of the Lie algebras. This talk will focus on different choices of basis for sl(2) that make transparent connections with the modular group, the braid group on 3 strands and its representations, hyperbolic Kac-Moody Lie algebras, and beyond. These bases arose in a natural way from combinatorial investigations of association schemes and tridiagonal pairs of linear transformations.