Abstract :

We narrate a tale of three interesting Lie algebras - the space sl_n of traceless square matrices of size 'n' and its infinite dimensional cousins - the "current" and "affine" Lie algebras. The affine algebra has a special infinite-dimensional representation ("the level 1 vacuum module"), successively approximated by finite-dimensional pieces called Demazure modules. We can view Demazure modules from two perspectives - as representations of the current algebra and of sl_n itself. This results in two disparate combinatorial models and bases for the same object. The talk will attempt to pictorially reconcile these points of view, resolve the tension and bring matters to a happy conclusion. This is based on joint work with Aritra Bhattacharya and TV Ratheesh.