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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 063, 26 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.063 (Mi sigma1745) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains

Sergey É. Derkachova, Karol K. Kozlowskib, Alexander N. Manashovac

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
b Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
c Institut für Theoretische Physik, Universität Hamburg, D-22761 Hamburg, Germany
Full-text PDF (515 kB) Citations (2)
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DOI: https://doi.org/10.3842/SIGMA.2021.063
Abstract: This work develops a new method, based on the use of Gustafson's integrals and on the evaluation of singular integrals, allowing one to establish the unitarity of the separation of variables transform for infinite-dimensional representations of rank one quantum integrable models. We examine in detail the case of the $\mathrm{SL}(2,\mathbb R)$ spin chains.
Keywords: spin chains, separation of variables, Gustafson's integrals.
Funding agency Grant number
Russian Science Foundation 19-11-00131
Deutsche Forschungsgemeinschaft MO 1801/4-1
KN 365/13-1
This work was supported by the Russian Science Foundation project No 19-11-00131 and by the DFG grants MO 1801/4-1, KN 365/13-1 (A.M.). The work of K.K.K. is supported by CNRS.
Received: March 8, 2021; in final form June 14, 2021; Published online June 25, 2021
Bibliographic databases:
Document Type: Article
MSC: 33C70, 81R12
Language: English
Citation: Sergey É. Derkachov, Karol K. Kozlowski, Alexander N. Manashov, “Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains”, SIGMA, 17 (2021), 063, 26 pp.
Citation in format AMSBIB
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\paper Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains
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\vol 17
\papernumber 063
\totalpages 26
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  • https://www.mathnet.ru/eng/sigma/v17/p63
    • This publication is cited in the following 2 articles:
    1. Alexander N. Manashov, “Unitarity of the SoV Transform for $\mathrm{SL}(2,\mathbb C)$ Spin Chains”, SIGMA, 19 (2023), 086, 24 pp.  mathnet  crossref
    2. Pavel V Antonenko, “The Gelfand–Tsetlin basis for infinite-dimensional representations of
      gln(C)”, J. Phys. A: Math. Theor., 55:22 (2022), 225201  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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    Abstract page:141
    Full-text PDF :45
    References:31
     
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