February 5, 2013



Mathematics Colloquium today

By Reta McDermott

Anton Khoroshkin from the Simons Center for Geometry and Physics at Stony Brook University, will present "Duality Theorems for Modules Over Current Algebras" at 2:30 p.m. today in 122 Cardwell Hall.

The algebra of regular functions on a finite group is isomorphic to the sum of V⊗ V^* over all irreducible representations V of G. Same decomposition exists for the regular (L2) functions on a compact Lie group.

In this talk, he will provide a similar description of regular function for a current Lie algebra, that is for the algebra g⊗C[t] with a semisimple Lie algebra g. In particular, he will describe a natural category of modules over current algebra generalizing the highest weight modules. He will also describe projective and simple modules in this category, and state certain multiplicity identities for them — the corresponding identity for characters is a specialization of Macdonald constant term identity.