A. F. Oskin, S. Z. Pakulyak, A. V. Silantiev, “On the universal weight function for the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_N)$”, Algebra i Analiz, 21:4 (2009), 196–240; St. Petersburg Math. J., 21:4 (2010), 651

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Algebra i Analiz, 2009, Volume 21, Issue 4, Pages 196–240 (Mi aa1149)

This article is cited in 17 scientific papers (total in 17 papers)

Research Papers

On the universal weight function for the quantum affine algebra

$U_q(\widehat{\mathfrak{gl}}_N)$

A. F. Oskin^a, S. Z. Pakulyak^ba, A. V. Silantiev^ac

^a Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow region, Russia
^b Institute for Theoretical and Experimental Physics, Moscow, Russia
^c Département de Mathématiques, Université d'Angers, Angers, France

Full-text PDF (478 kB) Citations (17)

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Abstract: The investigation is continued of the universal weight function for the quantum affine algebra

$U_q(\widehat{\mathfrak{gl}}_N)$ . Two recurrence relations are obtained for the universal weight function with the help of the method of projections. On the level of the evaluation representation of

$U_q(\widehat{\mathfrak{gl}}_N)$ , two recurrence relations are reproduced, which were calculated earlier for the off-shell Bethe vectors by combinatorial methods. One of the results of the paper is a description of two different but isomorphic currents or “new” realizations of the algebra

$U_q(\widehat{\mathfrak{gl}}_N)$ , corresponding to two different Gauss decompositions of the fundamental

$\mathrm{L}$ -operators.

Received: 22.07.2008

English version:
St. Petersburg Mathematical Journal, 2010, Volume 21, Issue 4, Pages 651–680
DOI: https://doi.org/10.1090/S1061-0022-2010-01110-5

Bibliographic databases:

Document Type: Article

MSC: 81R10

Language: Russian

Citation: A. F. Oskin, S. Z. Pakulyak, A. V. Silantiev, “On the universal weight function for the quantum affine algebra

$U_q(\widehat{\mathfrak{gl}}_N)$ ”, Algebra i Analiz, 21:4 (2009), 196–240; St. Petersburg Math. J., 21:4 (2010), 651–680

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/aa1149

https://www.mathnet.ru/eng/aa/v21/i4/p196

This publication is cited in the following 17 articles:

Maksim Kosmakov, Vitaly Tarasov, “New combinatorial formulae for nested Bethe vectors II”, Lett Math Phys, 115:1 (2025)
A. Liashyk, S. Pakuliak, “On the R-matrix realization of the quantum loop algebra. The case of Uq(Dn(2))”, Journal of Mathematical Physics, 65:12 (2024)
Liashyk A., Pakuliak S.Z., “Recurrence Relations For Off-Shell Bethe Vectors in Trigonometric Integrable Models”, J. Phys. A-Math. Theor., 55:7 (2022), 075201
Andrii Liashyk, Stanislav Pakuliak, “On the R-matrix realization of quantum loop algebras”, SciPost Phys., 12:5 (2022)
N. A. Slavnov, “Introduction to the nested algebraic Bethe ansatz”, SciPost Phys. Lect. Notes, 19 (2020), 1–53
Hutsalyuk A., Liashyk A., Pakuliak S.Z., Ragoucy E., Slavnov N.A., “Scalar Products and Norm of Bethe Vectors For Integrable Models Based on U-Q ((Gl)Over-Cap(M))”, SciPost Phys., 4:1 (2018), 006
Nikolay Gromov, Fedor Levkovich-Maslyuk, “New compact construction of eigenstates for supersymmetric spin chains”, J. High Energ. Phys., 2018:9 (2018)
A. A. Hutsalyuk, A. Liashyk, S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Current presentation for the super-Yangian double $DY(\mathfrak{gl}(m|n))$ and Bethe vectors”, Russian Math. Surveys, 72:1 (2017), 33–99
Gromov N., Levkovich-Maslyuk F., Sizov Grigory, “New Construction of Eigenstates and Separation of Variables For Su(N) Quantum Spin Chains”, J. High Energy Phys., 2017, no. 9, 111
Kozlowski K.K., Ragoucy E., “Asymptotic behaviour of two-point functions in multi-species models”, Nucl. Phys. B, 906 (2016), 241–288
S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with a $GL(3)$ trigonometric $R$-matrix: Highest coefficient”, Theoret. and Math. Phys., 178:3 (2014), 314–335
S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with the $GL(3)$ trigonometric $R$-matrix: General case”, Theoret. and Math. Phys., 180:1 (2014), 795–814
Pakuliak S., Ragoucy E., Slavnov N.A., “Bethe Vectors of Quantum Integrable Models Based On $U_q(\widehat{\mathfrak{gl}}_N)$”, J. Phys. A-Math. Theor., 47:10 (2014), 105202
Vitaly Tarasov, Alexander Varchenko, “Combinatorial Formulae for Nested Bethe Vectors”, SIGMA, 9 (2013), 048, 28 pp.
Samuel Belliard, Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Bethe Vectors of Quantum Integrable Models with $\mathrm{GL}(3)$ Trigonometric $R$-Matrix”, SIGMA, 9 (2013), 058, 23 pp.
Belliard S., Pakuliak S., Ragoucy E., Slavnov N.A., “Bethe Vectors of Gl(3)-Invariant Integrable Models”, J. Stat. Mech.-Theory Exp., 2013, P02020
Samuel Belliard, Stanislav Pakuliak, Eric Ragoucy, “Universal Bethe Ansatz and Scalar Products of Bethe Vectors”, SIGMA, 6 (2010), 094, 22 pp.

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

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