Geodesic
Gauss Coordinates vs Currents for the Yangian Doubles of the Classical Types
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider relations between Gauss coordinates of $T$-operators for the Yangian doubles of the classical types corresponding to the algebras $\mathfrak{g}$ of $A$, $B$, $C$ and $D$ series and the current generators of these algebras. These relations are important for the applications in the quantum integrable models related to $\mathfrak{g}$-invariant $R$-matrices and construction of the Bethe vectors in these models.
Keywords: Yangians, Drinfeld currents.
Mots-clés : Gauss decomposition 
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     author = {Andrii N. Liashyk and Stanislav Z. Pakuliak},
     title = {Gauss {Coordinates} vs {Currents} for the {Yangian} {Doubles} of the {Classical} {Types}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a119/}
}
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Andrii N. Liashyk; Stanislav Z. Pakuliak. Gauss Coordinates vs Currents for the Yangian Doubles of the Classical Types. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a119/

[1] Ding J. T., Frenkel I. B., “Isomorphism of two realizations of quantum affine algebra $U_q(\mathfrak{gl}(n))$”, Comm. Math. Phys., 156 (1993), 277–300 | DOI | MR | Zbl

[2] Drinfel'd V.G., “A new realization of Yangians and of quantum affine algebras”, Soviet Math. Dokl., 36 (1988), 212–216 | MR | Zbl

[3] Drinfel'd V.G., “Quantum groups”, J. Soviet Math., 41 (1988), 898–915 | DOI | MR | Zbl

[4] Enriquez B., Khoroshkin S., Pakuliak S., “Weight functions and Drinfeld currents”, Comm. Math. Phys., 276 (2007), 691–725, arXiv: math.QA/0610398 | DOI | MR | Zbl

[5] Hutsalyuk A., Liashyk A., Pakuliak S. Z., Ragoucy E., Slavnov N. A., “Current presentation for the double super-Yangian $DY (\mathfrak{gl}(m|n))$ and Bethe vectors”, Russian Math. Surveys, 72 (2017), 33–99, arXiv: 1611.09020 | DOI | MR | Zbl

[6] Hutsalyuk A., Liashyk A., Pakuliak S. Z., Ragoucy E., Slavnov N. A., “Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors”, J. Stat. Mech. Theory Exp., 2020 (2020), 093104, 31 pp., arXiv: 2005.09249 | DOI | MR

[7] Jing N., Liu M., Molev A., “Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$”, Comm. Math. Phys., 361 (2018), 827–872, arXiv: 1705.08155 | DOI | MR | Zbl

[8] Jing N., Liu M., Molev A., “Isomorphism between the $R$-matrix and Drinfeld presentations of quantum affine algebra: type $C$”, J. Math. Phys., 61 (2020), 031701, 41 pp., arXiv: 1903.00204 | DOI | MR | Zbl

[9] Jing N., Liu M., Molev A., “Isomorphism between the $R$-matrix and Drinfeld presentations of quantum affine algebra: types $B$ and $D$”, SIGMA, 16 (2020), 043, 49 pp., arXiv: 1911.03496 | MR | Zbl

[10] Jing N., Yang F., Liu M., “Yangian doubles of classical types and their vertex representations”, J. Math. Phys., 61 (2020), 051704, 39 pp., arXiv: 1810.06484 | DOI | MR | Zbl

[11] Khoroshkin S., Pakuliak S., “A computation of universal weight function for quantum affine algebra $U_q(\mathfrak{gl}_N)$”, J. Math. Kyoto Univ., 48 (2008), 277–321, arXiv: 0711.2819 | DOI | MR | Zbl

[12] Kulish P. P., Reshetikhin N. Yu., “Generalized Heisenberg ferromagnet and the Gross-Neveu model”, Sov. Phys. JETP, 53 (1981), 108–114 | MR

[13] Kulish P. P., Reshetikhin N.Yu., “Diagonalisation of $\mathrm{GL}(N)$ invariant transfer matrices and quantum $N$-wave system (Lee model)”, J. Phys. A: Math. Gen., 16 (1983), L591–L596 | DOI | MR | Zbl

[14] Liashyk A., Pakuliak S. Z., Algebraic Bethe ansatz for $\mathfrak{o}_{2n+1}$-invariant integrable models, arXiv: 2008.03664

[15] Liashyk A., Pakuliak S. Z., Ragoucy E., Slavnov N. A., “New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors”, J. Stat. Mech. Theory Exp., 2019 (2019), 044001, 24 pp., arXiv: 1810.00364 | DOI | MR

[16] Reshetikhin N. Yu., Semenov-Tian-Shansky M. A., “Central extensions of quantum current groups”, Lett. Math. Phys., 19 (1990), 133–142 | DOI | MR | Zbl

[17] Zamolodchikov A. B., Zamolodchikov A. B., “Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models”, Ann. Physics, 120 (1979), 253–291 | DOI | MR