×

The \(A_m^{(1)}\) Q-system. (English) Zbl 1448.81360

Summary: We propose a Q-system for the \(A_m^{(1)}\) quantum integrable spin chain. We also find compact determinant expressions for all the Q-functions, both for the rational and trigonometric cases.

MSC:

81R12 Groups and algebras in quantum theory and relations with integrable systems
82B23 Exactly solvable models; Bethe ansatz

References:

[1] Marboe, C. and Volin, D., J. Phys. A50, 204002 (2017), arXiv:1608.06504 [math-ph].
[2] Kazakov, V., Sorin, A. S. and Zabrodin, A., Nucl. Phys. B790, 345 (2008), arXiv:hep-th/0703147 [hep-th].
[3] Marboe, C. and Volin, D., J. Phys. A51, 165401 (2018), arXiv:1701.03704 [hep-th].
[4] Basso, B., Coronado, F., Komatsu, S., Lam, H. T., Vieira, P. and Zhong, D.-L., JHEP07, 082 (2019), arXiv:1701.04462 [hep-th].
[5] Suzuki, R., JHEP06, 055 (2017), arXiv:1703.05798 [hep-th].
[6] Ryan, P. and Volin, D., J. Math. Phys.60, 032701 (2019), arXiv:1810.10996 [math-ph].
[7] Coronado, F., JHEP01, 056 (2019), arXiv:1811.00467 [hep-th].
[8] Jacobsen, J. L., Jiang, Y. and Zhang, Y., JHEP03, 152 (2019), arXiv:1812.00447 [hep-th].
[9] Bajnok, Z., Jacobsen, J. L., Jiang, Y., Nepomechie, R. I. and Zhang, Y., JHEP06, 169 (2020), arXiv:2002.09019 [hep-th].
[10] Kuniba, A., Nakanishi, T. and Suzuki, J., J. Phys. A44, 103001 (2011), arXiv:1010.1344 [hep-th].
[11] Mukhin, E. and Varchenko, A., Central Eur. J. Math.1, 238 (2002), arXiv:math/0211321 [math.QA].
[12] Mukhin, E. and Varchenko, A., Geom. Topol. Monogr.13, 385 (2008), arXiv:math/0604048 [math.QA].
[13] Mukhin, E., Tarasov, V. and Varchenko, A., Transform. Groups19, 861 (2014), arXiv:1303.1578 [math.AG].
[14] Li, J. R. and Tarasov, V., J. Phys. Conf. Ser.411, 012020 (2013), arXiv:1210.2315 [math.QA].
[15] Bajnok, Z., Granet, E., Jacobsen, J. L. and Nepomechie, R. I., JHEP03, 177 (2020), arXiv:1910.07805 [hep-th].
[16] Nepomechie, R. I., J. Phys. A53, 294001 (2020), arXiv:1912.12702 [hep-th].
[17] Pronko, G. P. and Stroganov, Yu. G., J. Phys. A32, 2333 (1999), arXiv:hep-th/9808153 [hep-th].
[18] Pronko, G. P. and Stroganov, Yu. G., J. Phys. A33, 8267 (2000), arXiv:hep-th/9902085 [hep-th].
[19] Krichever, I., Lipan, O., Wiegmann, P. and Zabrodin, A., Commun. Math. Phys.188, 267 (1997), arXiv:hep-th/9604080 [hep-th]. · Zbl 0896.58035
[20] Kulish, P. P. and Reshetikhin, N. Yu., J. Exp. Theor. Phys.53, 108 (1981) [Zh. Eksp. Teor. Fiz.80, 214 (1981)].
[21] de Vega, H. J., Int. J. Mod. Phys. A04, 2371 (1989). · Zbl 0693.58045
[22] Tsuboi, Z., Nucl. Phys. B826, 399 (2010), arXiv:0906.2039 [math-ph].
[23] Tsuboi, Z., Nucl. Phys. B870, 92 (2013), arXiv:1109.5524 [hep-th].
[24] Mukhin, E., Tarasov, V. and Varchenko, A., Commun. Math. Phys.288, 1 (2009), arXiv:0706.0688 [math].
[25] Tarasov, V., Rev. Math. Phys.30, 1840018 (2018). · Zbl 1434.82030
[26] Jimbo, M., Commun. Math. Phys.102, 537 (1986). · Zbl 0604.58013
[27] Kulish, P. P., J. Sov. Math.35, 2648 (1986) [Zap. Nauchn. Semin.145, 140 (1985)]. · Zbl 0606.58054
[28] Sklyanin, E. K., J. Phys. A21, 2375 (1988). · Zbl 0685.58058
[29] de Vega, H. J. and Gonzalez Ruiz, A., J. Phys. A26, L519 (1993), arXiv:hep-th/9211114 [hep-th].
[30] de Vega, H. J. and Gonzalez-Ruiz, A., Mod. Phys. Lett. A9, 2207 (1994), arXiv:hep-th/9404141 [hep-th].
[31] Doikou, A. and Nepomechie, R. I., Nucl. Phys. B530, 641 (1998), arXiv:hep-th/9807065 [hep-th].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.