Pron’ko, G. P.; Stroganov, Yu. G. Bethe equations “On the wrong side of the equator”. (English. Russian original) Zbl 0957.82013 Theor. Math. Phys. 118, No. 3, 357-364 (1999); translation from Teor. Mat. Fiz. 118, No. 3, 452-461 (1999). Summary: The \(T\)-\(Q\) Baxter equations for the \(XXX\) \((XXZ)\) spin chain are analyzed. For each polynomial (trigonometric) solution of degree not exceeding \(N/2\), which provides a solution of the Bethe ansatz equations, there exists a second linearly independent polynomial solution of degree greater than \(N/2\). This second solution plays an essential role; in particular, all fusion relations follow from these two solutions. Cited in 1 Document MSC: 82B23 Exactly solvable models; Bethe ansatz Keywords:XXX spin chain; \(T\)-\(Q\) Baxter equations; Bethe ansatz equations; polynomial solution; fusion relations PDF BibTeX XML Cite \textit{G. P. Pron'ko} and \textit{Yu. G. Stroganov}, Theor. Math. Phys. 118, No. 3, 357--364 (1999; Zbl 0957.82013); translation from Teor. Mat. Fiz. 118, No. 3, 452--461 (1999) Full Text: DOI References: [1] H. Bethe,Z. Phys.,71, 205–226 (1931). · doi:10.1007/BF01341708 [2] L. D. Faddeev, ”How algebraic Bethe ansatz works for integrable model,” in:Les Houches Lectures, North-Holland, Amsterdam (1995), pp. 1–59; Preprint hep-th/9605187 (1996). [3] L. D. Faddeev and L. A. Takhtadzhyan,J. Sov. Math.,24, 241–267 (1984). · Zbl 0532.47009 · doi:10.1007/BF01087245 [4] R. J. Baxter,Stud. Appl. Math. L, 51–69 (1971). [5] R. J. Baxter,Ann. Phys.,70, 193–228 (1972). · Zbl 0236.60070 · doi:10.1016/0003-4916(72)90335-1 [6] R. J. Baxter,Ann. Phys.,76, 1–24 (1973);76, 25–47 (1973);76, 48–71 (1973). · Zbl 1092.82511 · doi:10.1016/0003-4916(73)90439-9 [7] V. V. Bazhanov, S. L. Lukyanov, and A. B. Zamolodchikov,Commun. Math. Phys.,177, 381–398 (1996);190, 247–278 (1997); ”Integrable structure of conformal field theory III. The Yang-Baxter relation,” Preprint hep-th/9805008 (1998). · Zbl 0851.35113 · doi:10.1007/BF02101898 [8] A. Antonov and B. Feigin, ”Quantum group representations and Baxter equation”, Preprint hep-th/9603105 (1996). [9] I. Krichever, O. Lipan, P. Wiegmann, and A. Zabrodin,Commun. Math. Phys.,188, 267–304 (1997). · Zbl 0896.58035 · doi:10.1007/s002200050165 [10] A. N. Kirillov and N. Yu. Reshetikhin,J. Phys. A,20, 1565–1585 (1987). · doi:10.1088/0305-4470/20/6/038 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.