Asymptotic Representations of Quantum Affine Superalgebras

We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modul...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2017
Main Author: Zhang, H.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/148732
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Asymptotic Representations of Quantum Affine Superalgebras / H. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Zhang, H.
author_facet Zhang, H.
citation_txt Asymptotic Representations of Quantum Affine Superalgebras / H. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.
first_indexed 2025-12-07T19:55:57Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T19:55:57Z
publishDate 2017
publisher Інститут математики НАН України
record_format dspace
spelling Zhang, H.
2019-02-18T18:16:12Z
2019-02-18T18:16:12Z
2017
Asymptotic Representations of Quantum Affine Superalgebras / H. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 17B37; 17B10; 81R50
DOI:10.3842/SIGMA.2017.066
https://nasplib.isofts.kiev.ua/handle/123456789/148732
We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.
The author thanks Vyjayanthi Chari, Giovanni Felder, David Hernandez, Masaki Kashiwara,
 Eugene Mukhin, Zengo Tsuboi, and Weiqiang Wang for interesting discussions. He is supported
 by the National Center of Competence in Research SwissMAP – The Mathematics of Physics
 of the Swiss National Science Foundation.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Asymptotic Representations of Quantum Affine Superalgebras
Article
published earlier
spellingShingle Asymptotic Representations of Quantum Affine Superalgebras
Zhang, H.
title Asymptotic Representations of Quantum Affine Superalgebras
title_full Asymptotic Representations of Quantum Affine Superalgebras
title_fullStr Asymptotic Representations of Quantum Affine Superalgebras
title_full_unstemmed Asymptotic Representations of Quantum Affine Superalgebras
title_short Asymptotic Representations of Quantum Affine Superalgebras
title_sort asymptotic representations of quantum affine superalgebras
url https://nasplib.isofts.kiev.ua/handle/123456789/148732
work_keys_str_mv AT zhangh asymptoticrepresentationsofquantumaffinesuperalgebras