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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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Additional Information

Vyjayanthi Chari
Affiliation: Department of Mathematics, University of California, Riverside, California 92521
Email: chari@math.ucr.edu

Andrew Pressley
Affiliation: Department of Mathematics, Kings College, London, WC 2R, 2LS, England, United Kingdom
Email: anp@mth.kcl.ac.uk

DOI: https://doi.org/10.1090/S1088-4165-01-00115-7
Received by editor(s): August 23, 2000
Published electronically: July 5, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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