February 5, 2013
Mathematics Colloquium today
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.