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Asymptotic representations and Drinfeld rational fractions

Published online by Cambridge University Press:  10 July 2012

David Hernandez
Institut de Mathématiques de Jussieu, Université Paris Diderot (Paris VII), 175 rue du Chevaleret, 75013 Paris, France (email:
Michio Jimbo
Department of Mathematics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan (email:
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We introduce and study a category of representations of the Borel algebra associated with a quantum loop algebra of non-twisted type. We construct fundamental representations for this category as a limit of the Kirillov–Reshetikhin modules over the quantum loop algebra and establish explicit formulas for their characters. We prove that general simple modules in this category are classified by n-tuples of rational functions in one variable which are regular and non-zero at the origin but may have a zero or a pole at infinity.

Research Article
Copyright © Foundation Compositio Mathematica 2012


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