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Highest ℓ-Weight Representations and Functional Relations
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- Фізико-технічні та математичні науки
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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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Highest ℓ-Weight Representations and Functional Relations
Інший ID:
2010 Mathematics Subject Classification: 17B37; 16T25; 17B10
DOI:10.3842/SIGMA.2017.043
DOI:10.3842/SIGMA.2017.043
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
390
Завантажень:
146
Анотація:
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.
