Bethe equations ``on the wrong side of the equator''
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 452-461

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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.
@article{TMF_1999_118_3_a15,
     author = {G. P. Pron'ko and Yu. G. Stroganov},
     title = {Bethe equations ``on the wrong side of the equator''},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {452--461},
     publisher = {mathdoc},
     volume = {118},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a15/}
}
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G. P. Pron'ko; Yu. G. Stroganov. Bethe equations ``on the wrong side of the equator''. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 3, pp. 452-461. http://geodesic.mathdoc.fr/item/TMF_1999_118_3_a15/