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SIGMA, 2017, Volume 13, 043, 31 pages (Mi sigma1243)  

This article is cited in 1 scientific paper (total in 1 paper)

Highest $\ell$-Weight Representations and Functional Relations

Khazret S. Nirovab, Alexander V. Razumovc

a Mathematics and Natural Sciences, University of Wuppertal, 42097 Wuppertal, Germany
b Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Ave. 7a, 117312 Moscow, Russia
c Institute for High Energy Physics, NRC ''Kurchatov Institute'', 142281 Protvino, Moscow region, Russia

Abstract: We discuss highest $\ell$-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 $\mathrm{U}_q(\mathcal L(\mathfrak{sl}_{l+1}))$ 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.

Keywords: quantum loop algebras; Verma modules; highest $\ell$-weight representations; $q$-oscillators.

Funding Agency Grant Number
Deutsche Forschungsgemeinschaft KL 645/10-1
Russian Foundation for Basic Research 14-01-91335__
16-01-00473_
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.


DOI: https://doi.org/10.3842/SIGMA.2017.043

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Bibliographic databases:

MSC: 17B37; 16T25; 17B10
Received: March 1, 2017; in final form June 6, 2017; Published online June 17, 2017
Language:

Citation: Khazret S. Nirov, Alexander V. Razumov, “Highest $\ell$-Weight Representations and Functional Relations”, SIGMA, 13 (2017), 043, 31 pp.

Citation in format AMSBIB
\Bibitem{NirRaz17}
\by Khazret~S.~Nirov, Alexander~V.~Razumov
\paper Highest $\ell$-Weight Representations and Functional Relations
\jour SIGMA
\yr 2017
\vol 13
\papernumber 043
\totalpages 31
\mathnet{http://mi.mathnet.ru/sigma1243}
\crossref{https://doi.org/10.3842/SIGMA.2017.043}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85021178402}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Khazret S. Nirov, Alexander V. Razumov, “Vertex Models and Spin Chains in Formulas and Pictures”, SIGMA, 15 (2019), 068, 67 pp.  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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