Yang-Baxter R-operators and parameter permutations

Nuclear Physics B

Volumn 785, Issue 3, 2007, Pages 263-285

  Derkachov, S ^a   Karakhanyan, D ^b   Kirschner, R ^c  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b YEREVAN PHYSICS INSTITUTE   (Armenia)

^c UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34848870568     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2007.05.022     Document Type: Article

References (28)

1. Baxter R. Partition function of the eight-vertex model. Ann. Phys. (N.Y.) 70 (1972) 193-228
2. Baxter R. Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg spin chain I. Ann. Phys. (N.Y.) 76 (1973) 1-24
3. Baxter R. Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg spin chain II. Ann. Phys. (N.Y.) 76 (1973) 25-47
4. Baxter R. Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg spin chain III. Ann. Phys. (N.Y.) 76 (1973) 48-71
5. Faddeev L.D., and Takhtadzhan L.A. The quantum method of the inverse problem and the Heisenberg XYZ model. Russian Math. Surveys 34 (1979) 11-68 (English translation)
6. Kulish P.P., and Sklyanin E.K. On the solutions of the Yang-Baxter equation. Zap. Nauchn. Sem. LOMI 95 (1980) 129
7. Kulish P.P., and Sklyanin E.K. Quantum spectral transform method. Recent developments. Lect. Notes Phys. 151 (1982) 61
8. Jimbo M. Introduction to the Yang-Baxter equation. Int. J. Mod. Phys. A 4 (1983) 3759
9. Jimbo M. Yang-Baxter equation in integrable systems. In: Jimbo M. (Ed). Adv. Ser. Math. Phys. vol. 10 (1990), World Scientific, Singapore
10. Faddeev L.D. How Algebraic Bethe Ansatz Works for Integrable Model, Les-Houches Lectures, 1995. hep-th/9605187
11. Kulish P.P., Reshetikhin N.Yu., and Sklyanin E.K. Yang-Baxter equation and representation theory. Lett. Math. Phys. 5 (1981) 393-403
12. Sklyanin E.K. On some algebraic structures related to Yang-Baxter equation. Funkts. Anal. Prilozh. 16 (1982) 27-34
13. Sklyanin E.K. On some algebraic structures related to Yang-Baxter equation: Representations of the quantum algebra. Funkts. Anal. Prilozh. 17 (1983) 34-48
14. Belitsky A.V., Braun V.M., Gorsky A.S., and Korchemsky G.P. Integrability in QCD and beyond. Int. J. Mod. Phys. A 19 (2004) 4715. hep-th/0407232
15. Krichever I., and Zabrodin A. Vacuum curves of elliptic L operators and Representations of Sklyanin algebra. solv-int/9801022
16. Zabrodin A. Commuting difference operators with elliptic coefficients from Baxter's vacuum vectors. J. Phys. A: Math. Gen. 33 (2000) 3825
17. Mumford D. Tata Lectures on Theta I. Progress in Mathematics (1983), Birkhäuser
18. 3. math.QA/9907061
19. Frenkel I., and Turaev V. Elliptic Solutions of the Yang-Baxter Equation and Modular Hypergeometric Functions, The Arnold-Gelfand Mathematical Seminars (1997), Birkhauser Boston, Cambridge, MA pp. 171-204
20. Rosengren H. Sklyanin invariant integration. math.QA/0405072
21. Gasper G. Elementary derivation of summation and transformation formulas for q-series. math.CA/9605230
22. Derkachov S. Factorization of the R-matrix. I. Zap. Nauchn. Sem. POMI 335 (2006) 134-163. math.QA/0503396
23. Derkachov S. Factorization of R-matrix and Baxter's Q-operator. math.QA/0507252
24. Derkachov S., and Manashov A. R-matrix and Baxter Q-operators for the noncompact SL (N, C) invariant spin chain. SIGMA 2 (2006) 084. nlin.SI/0612003
25. Derkachov S., and Manashov A. Baxter operators for the quantum s l (3) invariant spin chain. J. Phys. A 39 (2006) 13171. nlin.SI/0604018
26. Derkachov S., Karakhanyan D., and Kirschner R. Baxter Q-operators of the XXZ chain and R-matrix factorization. Nucl. Phys. B 738 (2006) 368-390. hep-th/0511024
27. Karakhanyan D., Kirschner R., and Mirumyan M. Universal R operator with deformed conformal symmetry. Nucl. Phys. B 636 (2002) 529. nlin.SI/0111032
28. Derkachov S.E., Korchemsky G.P., and Manashov A.N. Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables. Nucl. Phys. B 617 (2001) 375. hep-th/0107193