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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Received by editor(s):
August 23, 2000

Published electronically:
July 5, 2001

Article copyright:
© Copyright 2001
American Mathematical Society