Geodesic
The $R$-matrix factorization, $Q$-operator, and variable separation
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 204-217 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show a connection between the $R$-matrix factorization, the Baxter $Q$-operator, and separation of variables in the example of an integrable spin chain with the $SL(2,\mathbb{C})$ symmetry group.
Keywords: Yang–Baxter equation, $Q$-operator, separation of variables. 
@article{TMF_2011_169_2_a2,
     author = {S. \`E. Derkachev},
     title = {The~$R$-matrix factorization, $Q$-operator, and variable separation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {204--217},
     year = {2011},
     volume = {169},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a2/}
}
TY  - JOUR
AU  - S. È. Derkachev
TI  - The $R$-matrix factorization, $Q$-operator, and variable separation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 204
EP  - 217
VL  - 169
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a2/
LA  - ru
ID  - TMF_2011_169_2_a2
ER  - 
%0 Journal Article
%A S. È. Derkachev
%T The $R$-matrix factorization, $Q$-operator, and variable separation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 204-217
%V 169
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a2/
%G ru
%F TMF_2011_169_2_a2
S. È. Derkachev. The $R$-matrix factorization, $Q$-operator, and variable separation. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 204-217. http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a2/

[1] E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev, TMF, 40:2 (1979), 194–220 | DOI | MR

[2] L. I. Takhtadzhyan, L. D. Faddeev, UMN, 34:5(209) (1979), 13–63 | DOI | MR

[3] P. P. Kulish, E. K. Sklyanin, “Quantum spectral transform method recent developments”, Integrable Quantum Field Theories, Proceedings of the Symposium Held at Tvarminne (Finland, 23–27 March, 1981), Lecture Notes in Physics, 151, eds. J. Hietarinta, C. Montonen, 1982, 61–119 | DOI | MR | Zbl

[4] E. K. Sklyanin, “Quantum inverse scattering method. Selected topics”, Quantum Group and Quantum Integrable Systems, Nankai Lectures in Mathematical Physics, ed. Mo-Lin Ge, World Scientific, River Edge, NJ, 1992, 63–97, arXiv: hep-th/9211111 | MR

[5] L. D. Faddeev, “How the algebraic Bethe ansatz works for integrable models”, Quantum Symmetries. Proceedings of the Les Houches Summer School. Session LXIV (Les Houches, France, August 1 – September 8, 1995), eds. A. Connes, K. Gawedzki, J. Zinn-Justin, North-Holland, Amsterdam, 1998, 149–219 | MR | Zbl

[6] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR | MR | Zbl

[7] V. Pasquier, M. Gaudin, J. Phys. A, 25:20 (1992), 5243–5252 | DOI | MR | Zbl

[8] E. K. Sklyanin, Prog. Theor. Phys. Suppl., 118 (1995), 35–60, arXiv: solv-int/9504001 | DOI | MR | Zbl

[9] V. V. Bazhanov, S. L. Lukyanov, A. B. Zamolodchikov, Commun. Math. Phys., 177:2 (1996), 381–398, arXiv: ; 190:2 (1997), 247–278, arXiv: ; 200:2 (1999), 297–324, arXiv: hep-th/9412229hep-th/9604044hep-th/9805008 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[10] S. M. Khoroshkin, V. N. Tolstoy, Commun. Math. Phys., 141:3 (1991), 599–617 ; Lett. Math. Phys., 24:3 (1992), 231–244 ; S. M. Khoroshkin, A. A. Stolin, V. N. Tolstoy, Modern Phys. Lett. A, 10:19 (1995), 1375–1392, arXiv: hep-th/9404038 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[11] S. É. Derkachev, “Factorization of the R-matrix and Baxter's Q-operator”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 20, Zap. nauchn. sem. POMI, 347, POMI, SPb., 2007, 144–166, arXiv: math.qa/0507252 | DOI | MR

[12] S. É. Derkachov, A. N. Manashov, J. Phys. A, 39:16 (2006), 4147–4159, arXiv: nlin.si/0512047 | DOI | MR | Zbl

[13] S. E. Derkachëv, A. N. Manashov, Algebra i analiz, 21:4 (2009), 1–94 | DOI | MR | Zbl

[14] L. N. Lipatov, Pisma v ZhETF, 59:9 (1994), 571–574; L. N. Lipatov, Nucl. Phys. B, 548:1–3 (1999), 328–362, arXiv: hep-ph/9812336 | DOI

[15] L. D. Faddeev, G. P. Korchemsky, Phys. Lett. B, 342:1–4 (1995), 311–322, arXiv: hep-th/9404173 | DOI

[16] D. R. Karakhanyan, R. Kirschner, YaF, 65:8 (2002), 1539–1550, arXiv: ; Fortschr. Phys., 48:1–3 (2000), 139–142, arXiv: hep-th/9902147hep-th/9902031 | DOI | 3.0.CO;2-S class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[17] S. É. Derkachov, G. P. Korchemsky, A. N. Manashov, Nucl. Phys. B, 617:1–3 (2001), 375–440, arXiv: hep-th/0107193 | DOI | MR | Zbl

[18] I. M. Gelfand, M. I. Graev, N. Ya. Vilenkin, Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Obobschennye funktsii, 5, Fizmatlit, M., 1962 | MR

[19] P. P. Kulish, N. Yu. Reshetikhin, E. K. Sklyanin, Lett. Math. Phys., 5:5 (1981), 393–403 | DOI | MR | Zbl

[20] A. P. Isaev, Nucl. Phys. B, 662:3 (2003), 461–475, arXiv: hep-th/0303056 | DOI | MR | Zbl