Geodesic
On one ansatz for $\mathrm{sl}_2$-invariant $R$-matrices
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 19, Tome 335 (2006), pp. 100-118 Cet article a éte moissonné depuis la source Math-Net.Ru

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The spectral decomposition of regular $\mathrm{sl}_2$-invariant $R$-matrices $R(\lambda)$ is studied by means of the method of reduction of the Yang–Baxter equation onto subspaces of a given spin. Restrictions on the possible structure of several highest coefficients in the spectral decomposition are derived. The origin and structure of the exceptional solution in the case of spin $s=3$ are explained. An analogous analysis is performed for constant $R$-matrices. In particular, it is shown that the permutation matrix $\mathbb P$ is a “rigid” solution. 
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     title = {On one ansatz for $\mathrm{sl}_2$-invariant $R$-matrices},
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A. G. Bytsko. On one ansatz for $\mathrm{sl}_2$-invariant $R$-matrices. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 19, Tome 335 (2006), pp. 100-118. http://geodesic.mathdoc.fr/item/ZNSL_2006_335_a5/

[1] P. P. Kulish, E. K. Sklyanin, “Quantum spectral transform method. Recent developments”, Lect. Notes Physics, 151, 1982, 61–119 | MR | Zbl

[2] L. D. Faddeev, “How algebraic Bethe ansatz works for integrable model”, Symétries quantiques (Les Houches 1995), North-Holland, Amsterdam, 1998, 149–219 ; arXiv: /hep-th/9605187 | MR | Zbl

[3] A. G. Bytsko, “O $U_q(\mathrm{Sl}_2)$-invariantnykh $R$-matritsakh dlya starshikh spinov”, Algebra i analiz, 17:3 (2005), 24–46 | MR

[4] T. Kennedy, “Solutions of the Yang–Baxter equation for isotropic quantum spin chains”, J. Phys., 25 (1992), 2809–2817 | MR | Zbl

[5] L. Bidenkharn, Dzh. Lauk, Uglovoi moment v kvantovoi mekhanike, Mir, M., 1984

[6] P. P. Kulish, N. Yu. Reshetikhin, E. K. Sklyanin, “Yang–Baxter equations and representation theory, I”, Lett. Math. Phys., 5 (1981), 393–403 | DOI | MR | Zbl