Asymptotic representations and Drinfeld rational fractions

Abstract

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 we 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.

32 pages; accepted for publication in Compositio Mathematica

References in corpus (2)

• Baxter's Q-operators for supersymmetric spin chains
• The Baxter's Q-operator for the W-algebra $W_N$

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