Weyl modules for classical and quantum affine algebras

Abstract

We introduce and study the notion of a Weyl module for the classical affine algebras, these modules are universal finite-dimensional highest weight modules. We conjecture that the modules are the classical limit of a family of irreducible modules of the quantum affine algebra, and prove the conjecture in the case of s l 2 sl_2 . The conjecture implies also that the Weyl modules are the classical limits of the standard modules introduced by Nakajima and further studied by Varagnolo and Vasserot.