An integrable structure related with tridiagonal algebras

Nuclear Physics B

Volumn 705, Issue 3, 2005, Pages 605-619

  Baseilhac, Pascal ^a  

^a UNIVERSITÉ DE TOURS   (France)

Author keywords

Dolan Grady relations; Massive integrable models; Onsager algebra; Quadratic algebras; Tridiagonal algebra; Tridiagonal pair

Indexed keywords

EID: 11344256642     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2004.11.014     Document Type: Article

References (41)

1. P. Terwilliger Two relations that generalize the q-Serre relations and the Dolan-Grady relations math.QA/0307016
2. P. Terwilliger J. Algebraic Combin. 2 1993 177
3. T. Ito K. Tanabe P. Terwilliger Some algebra related to P- and Q-polynomial association schemes Proceedings of DIMACS Conference on Codes and Association Schemes Piscataway, NJ, 1999 DIMACS Series Discrete Mathematics Theoretical Computer Science vol. 56 2001 American Mathematical Society Providence, RI 167-192
4. L. Dolan M. Grady Phys. Rev. D 25 1982 1587
5. P. Terwilliger Linear Algebra Appl. 330 2001 149
6. P. Terwilliger R. Vidunas Leonard pairs and the Askey-Wilson relations math.QA/0305356
7. A.S. Zhedanov Mod. Phys. Lett. A 7 1992 1589
8. T. Ito P. Terwilliger Tridiagonal pairs and the quantum affine algebra U q ( sl 2 ̂ ) math.QA/0310042
9. V. Chari A. Pressley A Guide to Quantum Groups 1994 Cambridge Univ. Press Cambridge
10. P. Baseilhac Deformed Dolan-Grady relations in quantum integrable models hep-th/0404149
11. G. Lezter Coideal subalgebras and quantum symmetric pairs S. Montgomery H.J. Schneider New Directions in Hopf Algebras Mathematical Sciences Research Institute Publications vol. 43 2002 Cambridge Univ. Press Cambridge 117
12. S.-S. Roan, Onsager's algebra, loop algebra and chiral Potts model, Max Planck Institute für Mathematik, Preprint, 1991
13. E. Date S.-S. Roan J. Phys. A 33 2000 3275
14. I.V. Cherednik Teor. Mat. Fiz. 61 1984 55
15. E.K. Sklyanin J. Phys. A 21 1988 2375
16. P. Baseilhac K. Koizumi Nucl. Phys. B 649 2003 491
17. P.B. Wiegmann A.V. Zabrodin Nucl. Phys. B 451 1995 699
18. H.J. de Vega A. González-Ruiz J. Phys. A 27 1994 6129
19. L. Mezincescu R.I. Nepomechie Int. J. Mod. Phys. A 13 1998 2747
20. G.W. Delius N.J. MacKay Commun. Math. Phys. 233 2003 173
21. A. Doikou Boundary quantum group generators from the open transfer matrix math-ph/0402067
22. P. Baseilhac, A. Doikou, in preparation
23. D. Bernard A. LeClair Commun. Math. Phys. 142 1991 99
24. S. Ghoshal A.B. Zamolodchikov Int. J. Mod. Phys. A 9 1994 3841
25. L. Onsager Phys. Rev. 65 1944 117
26. B. Davies J. Phys. A 23 1990 2245-2261
27. B. Davies J. Math. Phys. 32 1991 2945
28. G. von Gehlen Int. J. Mod. Phys. B 16 2002 2129
29. R.J. Baxter Phys. Lett. A 133 1988 185
30. G. Albertini B.M. McCoy J.H.H. Perk Adv. Stud. Pure Math. 19 1989 1
31. R.J. Baxter V.V. Bazhanov J.H.H. Perk Int. J. Mod. Phys. B 4 1990 803
32. V.V. Bazhanov Yu.G. Stroganov J. Stat. Phys. 59 1990 799
33. G. von Gehlen V. Rittenberg Nucl. Phys. B 257 1985 351
34. J.H.H. Perk Star-triangle equations, quantum Lax operators, and higher genus curves Proceedings 1987 Summer Research Institute on Theta Functions Proceedings of Symposium in Pure Mathematics vol. 49 1989 American Mathematical Society Providence, RI 341-354
35. H. Au-Yang B.M. McCoy J.H.H. Perk S. Tang Solvable models in statistical mechanics and linobreak Riemann surfaces of genus greater than one M. Kashiwara T. Kawai Algebraic Analysis vol. 1 1988 Academic Press San Diego 29-40
36. C. Ahn K. Shigemoto Mod. Phys. Lett. A 6 1991 3509
37. S.M. Klishevich M.S. Plyushchay Nucl. Phys. B 628 2002 217
38. S.M. Klishevich M.S. Plyushchay J. Phys. A 36 2003 11299
39. V.V. Bazhanov S.L. Lukyanov A.B. Zamolodchikov Commun. Math. Phys. 177 1996 381
40. V.V. Bazhanov S.L. Lukyanov A.B. Zamolodchikov Commun. Math. Phys. 190 1997 247
41. V.V. Bazhanov S.L. Lukyanov A.B. Zamolodchikov Commun. Math. Phys. 200 1999 297