Highest ℓ-Weight Representations and Functional Relations

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13, випуск за цей рік
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dc.contributor.author	Nirov, K.S.
dc.contributor.author	Razumov, A.V.
dc.date.accessioned	2019-02-18T16:52:47Z
dc.date.available	2019-02-18T16:52:47Z
dc.date.issued	2017
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 17B37; 16T25; 17B10
dc.identifier.other	DOI:10.3842/SIGMA.2017.043
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148644
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Highest ℓ-Weight Representations and Functional Relations	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA