Geodesic
Solutions of the Yang equation with rational irreducible spectral curves
Izvestiya. Mathematics, Tome 42 (1994) no. 1, pp. 51-65 
V. I. Dragovich. Solutions of the Yang equation with rational irreducible spectral curves. Izvestiya. Mathematics, Tome 42 (1994) no. 1, pp. 51-65. http://geodesic.mathdoc.fr/item/IM2_1994_42_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The author studies rank 1 solutions of the Yang equation $\mathscr R^{12}\mathscr L^{13}\mathscr L^{'23}=\mathscr L^{'23}\mathscr L^{13}\mathscr R^{12}$ with rational irreducible spectral curves with ordinary double points. A complete list of the solutions is given, and it is shown that these solutions, which satisfy the Yang–Baxter equation, lead to the $R$-matrix of Cherednik.

[1] Krichever I. M., “Uravneniya Bakstera i algebraicheskaya geometriya”, Funkts. analiz, 15:2 (1981), 22–35 | MR | Zbl

[2] Krichever I. M., “Integrirovanie lineinykh uravnenii metodami algebraicheskoi geometrii”, Funkts. analiz, 11:1 (1977), 15–31 | Zbl

[3] Krichever I. M., “Kommutativnye koltsa lineinykh obyknovennykh differentsialnykh operatorov”, Funkts. analiz, 12:3 (1978), 20–31 | MR | Zbl

[4] Krichever I. M., Novikov S. P., “Golomorfnye rassloeniya nad rimanovymi poverkhnostyami i uravnenie KP1”, Funkts. analiz, 12:4 (1978), 41–52 | MR | Zbl

[5] Takhtadzhan L. A., Faddeev L. D., “Kvantovyi metod obratnoi zadachi i $XYZ$-model Geizenberga”, UMN, 34:5 (1979), 13–63 | MR

[6] Kulish P. P., Sklyanin E. K., “O resheniyakh uravneniya Yanga–Bakstera”, Differentsialnaya geometriya, gruppy Li i mekhanika, Zap. nauchn. sem. LOMI, 95, 1980, 129–160 | MR

[7] Belavin A. L., Drinfeld V. G., “O resheniyakh klassicheskogo uravneniya Yanga–Bakstera dlya prostykh algebr Li”, Funkts. analiz, 16:3 (1982), 1–29 | MR | Zbl

[8] Cherednik I. V., “Ob odnom metode postroeniya faktorizovannykh $S$-matrits v elementarnykh funktsiyakh”, TMF, 43:1 (1980), 117–119 | MR

[9] Dubrovin B. A., Malanyuk T. M., Krichever I. M., Makhankov V. G., “Tochnye resheniya nestatsionarnogo uravneniya Shredingera s samosoglasovannymi potentsialami”, Fizika EChAYa, 19:3 (1988), 579–622 | MR

[10] Cherednik I. V., “O nekotorykh $S$-matritsakh, svyazannykh s abelevymi mnogoobraziyami”, DAN SSSR, 249 (1979), 1095 | MR | Zbl