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 |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| 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| _version_ | 1862632105400336384 |
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| author | Nirov, K.S. Razumov, A.V. |
| author_facet | Nirov, K.S. Razumov, A.V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-30T12:17:05Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148644 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T12:17:05Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Highest ℓ-Weight Representations and Functional Relations Article published earlier |
| spellingShingle | Highest ℓ-Weight Representations and Functional Relations Nirov, K.S. Razumov, A.V. |
| title | 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_short | Highest ℓ-Weight Representations and Functional Relations |
| title_sort | highest ℓ-weight representations and functional relations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148644 |
| work_keys_str_mv | AT nirovks highestlweightrepresentationsandfunctionalrelations AT razumovav highestlweightrepresentationsandfunctionalrelations |