Weyl Modules for Classical and Quantum Affine algebras

TL;DR

This paper introduces Weyl modules for affine Lie algebras, conjectures their relation to quantum affine algebra representations, and proves key properties including irreducibility criteria and factorization, advancing understanding of finite-dimensional modules.

Contribution

It defines Weyl modules for affine Lie algebras, conjectures their classical limits correspond to quantum affine algebra representations, and proves irreducibility criteria and factorization theorems.

Findings

Proved the conjecture for affine sl_2.

Established irreducibility criteria for Weyl modules.

Proved a factorization theorem for these modules.

Abstract

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the quantum affine algebras. We prove this conjecture in the case of affine sl_2. We establish a criterion for these modules to be irreducible and prove a factorization theorem for them in the general case.