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: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| 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| _version_ | 1862736852489863168 |
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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.
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| first_indexed | 2025-12-07T19:55:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148732 |
| 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 |