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Yangians, quantum loop algebras and elliptic quantum groups Toledano Laredo, Valerio
Description
The Yangian Yg and quantum loop algebra Uq(Lg) of a complex semisimple Lie algebra g share very many similarities, and were long thought to have the same representations, though no precise relation between them existed until recently. I will explain how to construct a faithful functor from the finite-dimensional representations of Yg to those of Uq(Lg). The functor is entirely explicit, and governed by the monodromy of the abelian difference equations determined by the commuting fields of the Yangian. It yields a meromorphic, braided Kazhdan-Lusztig equivalence between finite-dimensional representations of the Yg and of U_q(Lg). A similar construction yields a faithful functor from representations of U_q(Lg) to those of the elliptic quantum group E_{q,t}(g) corresponding to g. This allows in particular a classification of irreducible finite-dimensional representations of E_{q,tau}(g), which was previously unknown. This is joint work with Sachin Gautam (Perimeter Institute).
Item Metadata
Title |
Yangians, quantum loop algebras and elliptic quantum groups
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-02-10T09:01
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Description |
The Yangian Yg and quantum loop algebra Uq(Lg) of a complex
semisimple Lie algebra g share very many similarities, and were
long thought to have the same representations, though no precise
relation between them existed until recently.
I will explain how to construct a faithful functor from the finite-dimensional
representations of Yg to those of Uq(Lg). The functor is entirely
explicit, and governed by the monodromy of the abelian difference
equations determined by the commuting fields of the Yangian. It
yields a meromorphic, braided Kazhdan-Lusztig equivalence between
finite-dimensional representations of the Yg and of U_q(Lg).
A similar construction yields a faithful functor from representations
of U_q(Lg) to those of the elliptic quantum group E_{q,t}(g) corresponding
to g. This allows in particular a classification of irreducible finite-dimensional
representations of E_{q,tau}(g), which was previously unknown.
This is joint work with Sachin Gautam (Perimeter Institute).
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Extent |
56 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Northeastern University
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Series | |
Date Available |
2016-08-11
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0307470
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International