Weyl modules for classical and quantum affine algebras

Chari, Vyjayanthi; Pressley, Andrew

doi:10.1090/S1088-4165-01-00115-7

Weyl modules for classical and quantum affine algebras

Authors: Vyjayanthi Chari and Andrew Pressley
Journal: Represent. Theory 5 (2001), 191-223
MSC (2000): Primary 81R50, 17B67
DOI: https://doi.org/10.1090/S1088-4165-01-00115-7
Published electronically: July 5, 2001
MathSciNet review: 1850556
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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 $sl_2$. 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.

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