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Relativistic Toda Chain with Boundary Interaction at Root of Unity
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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We apply the Separation of Variables method to obtain eigenvectors of commuting Hamiltonians in the quantum relativistic Toda chain at a root of unity with boundary interaction.
Keywords: quantum integrable model with boundary interaction; quantum relativistic Toda chain. 
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     author = {Nikolai Iorgov and Vladimir Roubtsov and Vitaly Shadura and Yuri Tykhyy},
     title = {Relativistic {Toda} {Chain} with {Boundary} {Interaction} at {Root} of {Unity}},
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     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a12/}
}
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Nikolai Iorgov; Vladimir Roubtsov; Vitaly Shadura; Yuri Tykhyy. Relativistic Toda Chain with Boundary Interaction at Root of Unity. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a12/

[1] Sklyanin E., “Separation of variable. New trends”, Prog. Theoret. Phys. Suppl., 118 (1995), 35–60 ; solv-int/9504001 | DOI | MR | Zbl

[2] Kharchev S., Lebedev D., “Integral representation for the eigenfunctions of quantum periodic Toda chain”, Lett. Math. Phys., 50 (1999), 53–77 ; hep-th/9910265 | DOI | MR | Zbl

[3] Kharchev S., Lebedev D., Semenov-Tian-Shansky M., “Unitary representations of $U_q({sl}(2,R))$, the modular double, and the multiparticle $q$-deformed Toda chains”, Comm. Math. Phys., 225 (2002), 573–609 ; hep-th/0102180 | DOI | MR | Zbl

[4] Kuznetsov V., “Separation of variables for the $D_n$ type periodic Toda lattice”, J. Phys. A: Math. Gen., 30 (1997), 2127–2138 ; solv-int/9701009 | DOI | MR | Zbl

[5] Iorgov N., Shadura V., “Wave functions of the Toda chain with boundary interactions”, Theor. Math. Phys., 142:2 (2005), 289–305 ; nlin.SI/0411002 | MR | Zbl

[6] Sklyanin E., “Boundary conditions for integrable quantum systems”, J. Phys. A: Math. Gen., 21 (1988), 2375–2389 | DOI | MR | Zbl

[7] von Gehlen G., Iorgov N., Pakuliak S., Shadura V., “Baxter–Bazhanov–Stoganov model: separation of variables and Baxter equation”, J. Phys. A: Math. Gen., 39 (2006), 7257–7282 ; nlin.SI/0603028 | DOI | MR | Zbl

[8] Iorgov N., “Eigenvectors of open Bazhanov–Stroganov quantum chain”, SIGMA, 2 (2006), 019, 10 pp., ages ; nlin.SI/0602010 | MR | Zbl

[9] Bazhanov V. V., Stroganov Yu. G., “Chiral Potts model as a descendant of the six-vertex model”, J. Statist. Phys., 59 (1990), 799–817 | DOI | MR | Zbl

[10] , J. Math. Sci. (New York), 85, 1997 hep-th/9410066 | DOI | MR

[11] Pakuliak S., Sergeev S., “Quantum relativistic Toda chain at root of unity: isospectrality, modified $Q$-operator and functional Bethe ansatz”, Int. J. Math. Math. Sci., 31 (2002), 513–554 ; nlin.SI/0205037 | DOI | MR

[12] Enriquez B., Rubtsov V., “Commuting families in skew fields and quantization of Beauville's fibrations”, Duke Math. J., 82 (2003), 197–219 ; math.AG/0112276 | MR

[13] Sergeev S., “Coefficient matrices of a quantum discrete auxiliary linear problem”, Zap. Nauchn. Sem. POMI, 269, no. 16, 2000, 292–307 (in Russian) | MR | Zbl

[14] Babelon O., Talon M., “Riemann surfaces, separation of variables and classical and quantum integrability”, Phys. Lett. A, 312 (2003), 71–77 ; hep-th/0209071 | DOI | MR | Zbl

[15] Kuznetsov V. B., Tsiganov A. V., “Infinite series of Lie algebras and boundary conditions for integrable systems”, J. Sov. Math., 59 (1992), 1085–1092 | DOI | MR

[16] Kuznetsov V. B., Tsiganov A. V., Separation of variables for the quantum relativistic Toda lattices, Report 94-07, Mathematical Preprint, University of Amsterdam, 1994; hep-th/9402111

[17] Kuznetsov V. B., Jorgensen M. F., Christiansen P. L., “New boundary conditions for integrable lattices”, J. Phys. A: Math. Gen., 28 (1995), 4639–4654 ; hep-th/9503168 | DOI | MR | Zbl

[18] de Vega H. J., Gonzalez-Ruiz A., “Boundary $K$-matrices for the XYZ, XXZ and XXX spin chains”, J. Phys. A: Math. Gen., 28 (1994), 6129–6141 | DOI | MR

[19] Bazhanov V. V., Baxter R. J., “Star-triangle relation for a three dimensional model”, J. Statist. Phys., 71 (1993), 839–864 ; hep-th/9212050 | DOI | MR

[20] Bugrij A. I., Iorgov N. Z., Shadura V. N., “Alternative method of calculating the eigenvalues of the transfer matrix of the $\tau_2$ model for $N=2$”, JETP Lett., 119:2 (2005), 311–315 | DOI