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International Conference dedicated to the 60-th birthday of Boris Feigin "Representation Theory and applications to Combinatorics, Geometry and Quantum Physics"
December 15, 2013 10:00–10:50, Moscow, Independent University of Moscow
 


From Yangians to quantum loop algebras via abelian difference equations

V. Toledano Laredo
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V. Toledano Laredo


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Abstract: The finite-dimensional representations of the Yangian $Y_h(g)$ and quantum loop algebra $U_q(Lg)$ of a complex, semisimple Lie algebra have long been known to share many similar features. Assuming that $q$ is not a root of unity, I will explain how to construct an equivalence of categories between finite-dimensional representations of $U_q(Lg)$ and an explicit subcategory of finite-dimensional representations of $Y_h(g)$. This equivalence is governed by the monodromy of an additive, abelian difference equation, and can be upgraded to a meromorphic tensor equivalence.
This is joint work with Sachin Gautam, and is based on: arXiv: 1310.7318 and arXiv: 1012.3687.

Language: English

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