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Spinor Representations of Orthogonal and Symplectic Yangians

  • PHYSICS OF ELEMENTARY PARTICLES AND ATOMIC NUCLEI. THEORY
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Abstract

We consider the explicit spinor \(R\) matrices of low rank orthogonal algebras and the corresponding \(RTT\) algebras using the new approach to calculation of spinorial \(R\) matrix. We also discuss the Algebraic Bethe Ansatz for spinor and vector monodromy matrices.

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REFERENCES

  1. L. D. Faddeev, E. K. Sklyanin, and L. A. Takhtajan, “The quantum inverse problem method. 1,” Theor. Math. Phys. 40, 688 (1980).

    MATH  Google Scholar 

  2. V. O. Tarasov, L. A. Takhtajan, and L. D. Faddeev, “Local Hamiltonians for integrable quantum models on a lattice,” Theor. Math. Phys. 57, 163 (1983).

    Article  MathSciNet  Google Scholar 

  3. P. P. Kulish and E. K. Sklyanin, “Quantum spectral transform method. Recent developments,” Lect. Notes Phys. 151, 61–119 (1982).

  4. L. D. Faddeev, “How algebraic Bethe ansatz works for integrable model,” in Quantum Symmetries/Symetries Quantiques, Proceedings of the 64th Les-Houches Summer School, Ed. by A. Connes, K. Kawedzki, and J. Zinn-Justin (North-Holland, Amsterdam, 1998), pp. 149–211; hep-th/9605187.

  5. N. Yu. Reshetikhin, “Integrable models of quantum one-dimensional models with O(n) and Sp(2k) symmetry,” Theor. Math. Fiz. 63, 347–366 (1985).

    Google Scholar 

  6. N. Yu. Reshetikhin, “Algebraic Bethe ansatz for SO(N)-invariant transfer matrices,” J. Sov. Math. 54, 940 (1991)

    Article  MathSciNet  Google Scholar 

  7. A. B. Zamolodchikov and Al. B. Zamolodchikov, “Factorized S matrices in two-dimensions as the exact solutions of certain relativistic quantum field models,” Ann. Phys. 120, 253 (1979).

    Article  ADS  Google Scholar 

  8. B. Berg, M. Karowski, P. Weisz, and V. Kurak, “Factorized U(n) symmetric S matrices in two dimensions,” Nucl. Phys. B 134, 125 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  9. R. Shankar and E. Witten, “The S-matrix of the kinks of the \({{(\bar {\psi }\psi )}^{2}}\) model,” Nucl. Phys. B 141, 349–363 (1978).

    Article  ADS  Google Scholar 

  10. D. Chicherin, S. Derkachov, and A. P. Isaev, “Spinorial R-matrix,” J. Phys. A 46, 485 201 (2013); arXiv: 1303.4929 [math-ph].

    Article  MathSciNet  Google Scholar 

  11. A. P. Isaev, D. Karakhanyan, and R. Kirschner, “Orthogonal and symplectic Yangians and Yang–Baxter R-operators,” Nucl. Phys. B 904, 124–147 (2016); arXiv: 1511.06152; J. Fuksa, A. P. Isaev, D. Karakhanyan, and R. Kirschner, “Yangians and Yang–Baxter R-operators for ortho-symplectic superalgebras,” Nucl. Phys. B 917, 44 (2017); arXiv: 1612.04713 [math-ph]. https://doi.org/10.1016/j.nuclphysb.2017.01.029

  12. C. Burdik and O. Navrátil, “Nested Bethe ansatz for the RTT algebra of sp(4) type,” Theor. Math. Phys. 198, 1 (2019). https://doi.org/10.1134/S004057791901001X

    Article  MathSciNet  MATH  Google Scholar 

  13. N. Jing, M. Liu, and F. Yang, “Double Yangians of the classical types and their vertex representations,” arXiv: 1810.06484 [math.QA]

  14. A. Liashyk, S. Z. Pakuliak, E. Ragoucy, and N. A. Slavnov, “Bethe vectors for orthogonal integrable models,” arXiv: 1906.03202; A. Liashyk, S. Z. Pakuliak, E. Ragoucy, and N. A. Slavnov, “New symmetries of gl(N)-invariant Bethe vectors,” J. Stat. Mech.: Theory Exp., 044001 (2019).

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Funding

This work is partially supported by the Armenian State Committee of Science grant 18T-132C1 and by Regional Training Network on Theoretical Physics sponsored by Volkswagenstiftung Contract no. 86 260.

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Correspondence to D. Karakhanyan.

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Karakhanyan, D. Spinor Representations of Orthogonal and Symplectic Yangians. Phys. Part. Nuclei Lett. 17, 794–802 (2020). https://doi.org/10.1134/S1547477120050180

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  • DOI: https://doi.org/10.1134/S1547477120050180

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