Highest ℓ-Weight Representations and Functional Relations

We discuss highest ℓ-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and q-oscillator representations of the positive Borel subalgebras of the quantum group Uq(L(sll₊₁)) for arbitra...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2017
Hauptverfasser: Nirov, K.S., Razumov, A.V.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2017
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/148644
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Highest ℓ-Weight Representations and Functional Relations / K.S. Nirov, A.V. Razumov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 40 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-148644
record_format dspace
spelling Nirov, K.S.
Razumov, A.V.
2019-02-18T16:52:47Z
2019-02-18T16:52:47Z
2017
Highest ℓ-Weight Representations and Functional Relations / K.S. Nirov, A.V. Razumov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 40 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 17B37; 16T25; 17B10
DOI:10.3842/SIGMA.2017.043
https://nasplib.isofts.kiev.ua/handle/123456789/148644
We discuss highest ℓ-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and q-oscillator representations of the positive Borel subalgebras of the quantum group Uq(L(sll₊₁)) for arbitrary values of l. Our article has partially the nature of a short review, but it also contains new results. These are the expressions for the L-operators, and the exact relationship between different representations, as a byproduct resulting in certain conclusions about functional relations.
This paper is a contribution to the Special Issue on Recent Advances in Quantum Integrable Systems. The full collection is available at http://www.emis.de/journals/SIGMA/RAQIS2016.html. We are grateful to H. Boos, F. G¨ohmann and A. Kl¨umper for discussions. This work was supported in part by the Deutsche Forschungsgemeinschaft in the framework of the research group FOR 2316, by the DFG grant KL 645/10-1, and by the RFBR grants # 14-01-91335 and # 16-01-00473. Kh.S.N. is grateful to the RAQIS’16 Organizers for the invitation and hospitality during the Conference “Recent Advances in Quantum Integrable Systems”, August 22–26, 2016, at the University of Geneva.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Highest ℓ-Weight Representations and Functional Relations
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Highest ℓ-Weight Representations and Functional Relations
spellingShingle Highest ℓ-Weight Representations and Functional Relations
Nirov, K.S.
Razumov, A.V.
title_short Highest ℓ-Weight Representations and Functional Relations
title_full Highest ℓ-Weight Representations and Functional Relations
title_fullStr Highest ℓ-Weight Representations and Functional Relations
title_full_unstemmed Highest ℓ-Weight Representations and Functional Relations
title_sort highest ℓ-weight representations and functional relations
author Nirov, K.S.
Razumov, A.V.
author_facet Nirov, K.S.
Razumov, A.V.
publishDate 2017
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We discuss highest ℓ-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and q-oscillator representations of the positive Borel subalgebras of the quantum group Uq(L(sll₊₁)) for arbitrary values of l. Our article has partially the nature of a short review, but it also contains new results. These are the expressions for the L-operators, and the exact relationship between different representations, as a byproduct resulting in certain conclusions about functional relations.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/148644
citation_txt Highest ℓ-Weight Representations and Functional Relations / K.S. Nirov, A.V. Razumov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 40 назв. — англ.
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