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Asymptotic representations and Drinfeld rational fractions. (English) Zbl 1266.17010

The authors study a certain analogue of the category \(\mathcal{O}\) for the Borel algebra associated with a quantum loop algebra of untwisted type. Simple modules in this category are classified using Drinfeld rational functions. They are infinite dimensional in general but have finite dimensional weight spaces. Certain “fundamental” modules in this category are constructed as limits of Kirillov-Reshetikhin modules over the quantum loop algebra. The authors give an explicit formula for characters of these fundamental modules (this is the main result of the paper). In fact, some of the fundamental modules admit an action of a larger algebra, which the authors call the asymptotic algebra and which is of independent interest.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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