Asymptotic representations and Drinfeld rational fractions
By D. Hernandez, Michio Jimbo. Compositio Mathematica, 2011
130 citations recorded by the source corpus.
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 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5d8ac50f06b781fa588fb4f97f9ca0590f0b8810
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Citations in the corpus
- Quantum Geometry and Quiver Gauge Theories (2013, methodology): “[138] D. Hernandez and M. Jimbo, “Asymptotic representations and Drinfeld rational fractions,” ArXiv e-prints (Apr., 2011) , arXiv:1104.1891 [math.”
- BAXTER'S RELATIONS AND SPECTRA OF QUANTUM INTEGRABLE MODELS (2013, methodology): “damental representation L+ i,a. This is an infinite-dimensional representation of the Borel subalgebra (in the Kac– Moody sense) Uq(b) of Uq(g) that was introduced by M. Jimbo and the second author in [HJ]. In order to explain what it is, recall the classification of irreducible finite-dimensional repr”