Аннотация:
The problem of constructing the SL(N,C) invariant solutions to the Yang–Baxter equation is considered. The solutions (R-operators) for arbitrarily principal series representations of SL(N,C) are obtained in an explicit form. We construct the commutative family of the operators Qk(u) which can be identified with the Baxter operators for the noncompact SL(N,C) spin magnet.
Образец цитирования:
Sergey É Derkachov, Alexander N. Manashov, “R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain”, SIGMA, 2 (2006), 084, 20 pp.
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\by Sergey \'E Derkachov, Alexander N.~Manashov
\paper $\mathcal R$-Matrix and Baxter $\mathcal Q$-Operators for the Noncompact $\mathrm{SL}(N,\mathbb C)$ Invariant Spin Chain
\jour SIGMA
\yr 2006
\vol 2
\papernumber 084
\totalpages 20
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\crossref{https://doi.org/10.3842/SIGMA.2006.084}
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Эта публикация цитируется в следующих 38 статьяx:
Yury A. Neretin, “On Derkachov–Manashov R-matrices for the principal series of unitary representations”, Journal of Mathematical Physics, 65:5 (2024)
Nikolay Gromov, Nicolò Primi, Paul Ryan, “Form-factors and complete basis of observables via separation of variables for higher rank spin chains”, J. High Energ. Phys., 2022:11 (2022)
Tsuboi Z., “Universal Baxter Tq-Relations For Open Boundary Quantum Integrable Systems”, Nucl. Phys. B, 963 (2021), 115286
Ferrando G., Frassek R., Kazakov V., “Qq-System and Weyl-Type Transfer Matrices in Integrable So(2R) Spin Chains”, J. High Energy Phys., 2021, no. 2, 193
M. V. Babich, “On Extensions of Canonical Symplectic Structure from Coadjoint Orbit of Complex General Linear Group”, J Math Sci, 257:4 (2021), 442
Yury A. Neretin, “Barnes–Ismagilov Integrals and Hypergeometric Functions of the Complex Field”, SIGMA, 16 (2020), 072, 20 pp.
Babich V M., “On Canonical Parametrization of Phase Spaces of Isomonodromic Deformation Equations”, Geometric Methods in Physics Xxxvii, Trends in Mathematics, eds. Kielanowski P., Odzijewicz A., Previato E., Birkhauser Verlag Ag, 2020, 3–12
Rouven Frassek, Vasily Pestun, “A Family of GLr Multiplicative Higgs Bundles on Rational Base”, SIGMA, 15 (2019), 031, 42 pp.
Tsuboi Z., “A Note on Q-Oscillator Realizations of U-Q(Gl(M|N)) For Baxter Q-Operators”, Nucl. Phys. B, 947 (2019), UNSP 114747
M. V. Babich, “On extensions of canonical symplectic structure from coadjoint orbit of complex general linear group”, Вопросы квантовой теории поля и статистической физики. 26, Зап. научн. сем. ПОМИ, 487, ПОМИ, СПб., 2019, 28–39
Gromov N., Kazakov V., Korchemsky G., Negro S., Sizov G., “Integrability of Conformal Fishnet Theory”, J. High Energy Phys., 2018, no. 1, 095
Hollands S. Lechner G., “S O (D, 1)-Invariant Yang–Baxter Operators and the dS/CFT Correspondence”, Commun. Math. Phys., 357:1, SI (2018), 159–202
Caetano J., Gurdogan O., Kazakov V., “Chiral Limit of N=4 SYM and ABJM and Integrable Feynman Graphs”, J. High Energy Phys., 2018, no. 3, 077
Chicherin D., Kazakov V., Loebbert F., Mueller D., Zhong D.-l., “Yangian Symmetry For Bi-Scalar Loop Amplitudes”, J. High Energy Phys., 2018, no. 5, 003
S. E. Derkachov, P. A. Valinevich, “Separation of variables for the quantum SL(3,C) spin magnet: eigenfunctions of Sklyanin B-operator”, Вопросы квантовой теории поля и статистической физики. 25, К 70-летию М. А. Семенова-Тян-Шанского, Зап. научн. сем. ПОМИ, 473, ПОМИ, СПб., 2018, 110–146; J. Math. Sci. (N. Y.), 242:5 (2019), 658–682
M. V. Babich, “О параметризации симплектической редукции декартова произведения коприсоединённых орбит комплексной общей линейной группы по её диагональному действию”, Зап. научн. сем. ПОМИ, 473 (2018), 7–16; M. V. Babich, “On parametrization of symplectic quotient of Cartesian product of coadjoint orbits of complex general linear group with respect to its diagonal action”, J. Math. Sci. (N. Y.), 242:5 (2019), 587–594
Frassek R., Marboe Ch., Meidinger D., “Evaluation of the Operatorial Q-System For Non-Compact Super Spin Chains”, J. High Energy Phys., 2017, no. 9, 018
M. V. Babich, “Birational Darboux coordinates on nilpotent coadjoint orbits classical complex Lie groups, Jordan blocks 2×2”, Вопросы квантовой теории поля и статистической физики. 24, Зап. научн. сем. ПОМИ, 465, ПОМИ, СПб., 2017, 5–12; J. Math. Sci. (N. Y.), 238:6 (2019), 763–768
М. В. Бабич, “Бирациональные координаты Дарбу на (ко)присоединенных орбитах группы GL(N,C)”, Функц. анализ и его прил., 50:1 (2016), 20–37; M. V. Babich, “Birational Darboux Coordinates on (Co)Adjoint Orbits of GL(N,C)”, Funct. Anal. Appl., 50:1 (2016), 17–30
M. V. Babich, “On birational Darboux coordinates on coadjoint orbits of classical complex Lie groups”, Теория представлений, динамические системы, комбинаторные методы. XXIV, Зап. научн. сем. ПОМИ, 432, ПОМИ, СПб., 2015, 36–57; J. Math. Sci. (N. Y.), 209:6 (2015), 830–844
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