S. E. Derkachov, P. A. Valinevich, “Separation of variables for the quantum $SL(3,\mathbb{C})$ spin magnet: eigenfunctions of Sklyanin $B$-operator”, Questions of quantum field theory and statistical physics. Part 25, Zap. Nauchn. Sem. POMI, 473, POMI, St. Petersburg, 2018, 110–146; J. Math. Sci. (N. Y.), 242:5 (2019), 658

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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 473, Pages 110–146 (Mi znsl6658)

This article is cited in 9 scientific papers (total in 9 papers)

Separation of variables for the quantum

$SL(3,\mathbb{C})$ spin magnet: eigenfunctions of Sklyanin

$B$ -operator

S. E. Derkachov, P. A. Valinevich

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Full-text PDF (332 kB) Citations (9)

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Abstract: The quantum

$SL(3, \mathbb{C})$ invariant spin magnet with infinite-dimensional principal series representation in local spaces is considered. We construct eigenfunctions of Sklyanin's

$B$ -operator which define the representation of separated variables of the model.

Key words and phrases: quantum spin chain, Separation of Variables, Yang–Baxter equation.

Funding agency	Grant number
Russian Science Foundation	14-11-00598
This work is supported by the Russian Science Foundation (project no. 14-11-00598).

Received: 15.10.2018

English version:
Journal of Mathematical Sciences (New York), 2019, Volume 242, Issue 5, Pages 658–682
DOI: https://doi.org/10.1007/s10958-019-04505-5

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: English

Citation: S. E. Derkachov, P. A. Valinevich, “Separation of variables for the quantum

$SL(3,\mathbb{C})$ spin magnet: eigenfunctions of Sklyanin

$B$ -operator”, Questions of quantum field theory and statistical physics. Part 25, Zap. Nauchn. Sem. POMI, 473, POMI, St. Petersburg, 2018, 110–146; J. Math. Sci. (N. Y.), 242:5 (2019), 658–682

Citation in format AMSBIB

\Bibitem{DerVal18}

\by S.~E.~Derkachov, P.~A.~Valinevich

\paper Separation of variables for the quantum $SL(3,\mathbb{C})$ spin magnet: eigenfunctions of Sklyanin $B$-operator

\inbook Questions of quantum field theory and statistical physics. Part~25

\serial Zap. Nauchn. Sem. POMI

\yr 2018

\vol 473

\pages 110--146

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl6658}

\transl

\jour J. Math. Sci. (N. Y.)

\yr 2019

\vol 242

\issue 5

\pages 658--682

\crossref{https://doi.org/10.1007/s10958-019-04505-5}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074194820}

Linking options:

https://www.mathnet.ru/eng/znsl6658

https://www.mathnet.ru/eng/znsl/v473/p110

This publication is cited in the following 9 articles:

Mikhail Alfimov, Gwenaël Ferrando, Vladimir Kazakov, Enrico Olivucci, “Checkerboard CFT”, J. High Energ. Phys., 2025:1 (2025)
Alexander N. Manashov, “Unitarity of the SoV Transform for $\mathrm{SL}(2,\mathbb C)$ Spin Chains”, SIGMA, 19 (2023), 086, 24 pp.
Xue Geng, Dianlou Du, Xianguo Geng, “Action-angle variables for the Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation”, Front. Phys., 11 (2023)
E. Olivucci, “Hexagonalization of fishnet integrals. Part I. Mirror excitations”, J. High Energy Phys., 2021, no. 11, 204
Sergey Derkachov, Enrico Olivucci, “Conformal quantum mechanics & the integrable spinning Fishnet”, J. High Energ. Phys., 2021:11 (2021)
Nikolay Gromov, Fedor Levkovich-Maslyuk, Paul Ryan, “Determinant form of correlators in high rank integrable spin chains via separation of variables”, J. High Energ. Phys., 2021:5 (2021)
Andrea Cavaglià, Nikolay Gromov, Fedor Levkovich-Maslyuk, “Separation of variables in AdS/CFT: functional approach for the fishnet CFT”, J. High Energ. Phys., 2021:6 (2021)
F. Levkovich-Maslyuk, “A review of the ads/cft quantum spectral curve”, J. Phys. A-Math. Theor., 53:28 (2020), 283004
A. Cavaglia, N. Gromov, F. Levkovich-Maslyuk, “Separation of variables and scalar products at any rank”, J. High Energy Phys., 2019, no. 9, 052

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

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References:	31

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