@article{TMF_1995_104_1_a1,
author = {A. V. Zabrodin},
title = {Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {8--24},
year = {1995},
volume = {104},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TMF_1995_104_1_a1/}
}
A. V. Zabrodin. Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 104 (1995) no. 1, pp. 8-24. http://geodesic.mathdoc.fr/item/TMF_1995_104_1_a1/
[1] P. Wiegmann, A. Zabrodin, Phys. Rev. Lett., 72 (1994), 1890 | DOI | MR
[2] P. Wiegmann, A. Zabrodin, NucJ. Phys., B 422 (1994), 495 | DOI | MR | Zbl
[3] J. Zak, Phys. Rev., 134 (1964), 1602 ; M.Ya. Azbel, Sov. Phys. JETP, 19 (1964), 634; G.H. Wannier, Phys. Status Solidi, 88 (1978), 757 ; D.R. Hofstadter, Phys. Rev., B14 (1976), 2239 ; D.J. Thouless, M. Kohmoto, P. Nightingale, M.den Nijs, Phys.Rev.Lett, 49 (1982), 405 | DOI | MR | Zbl | DOI | DOI | DOI
[4] P. Wiegmann, A .Zabrodin, Algebraization of difference eigenvalue equations related to $U_q(sl_a)$ \toappeaer in preparation
[5] L.D. Faddeev, Sov. Sci. Rev., C1 (1981), 107
[6] L.D. Faddeev, The Bethe ansatz, Andrejewski lectures, Preprint SFB 288, No 70, 1993
[7] E.K. Sklyanin, Zap. Nauchn. Semin. LOMI, 134, 1983, 112
[8] O.B. Zaslavsky, V.V. Ulyanov, Sov. Phys. JETP, 60 (1984), 991 ; Theor. Math. Phys., 71 (1987), 520 | MR | DOI
[9] V.G. Bagrov, A.S. Vshivtsev, preprint No 31, Tomsk, 1986 (unpublished)
[10] J .Patera, P. Winternitz, Journ. Math. Phys., 14 (1973), 1130 | DOI | MR | Zbl
[11] Y. Alhassid, F. Gursey, F .Iachello, Ann. Phys., 148 (1983), 346 | DOI | MR | Zbl
[12] A. Turbiner, Comm. Math. Phys., 118 (1988), 467 | DOI | MR | Zbl
[13] M.A. Shirman, Int. Journ. of Mod. Phys., A4 (1989), 2897 | DOI
[14] A. Turbiner, Lie algebras and quasi-exactly solvable differential equations, Preprint IFUNAM FT 94-57, 1994
[15] A. Ushveridze, Sov. Journal Part. Nucl., 20 (1989), 185 ; ibid. 23 (1992), 25 | MR | MR
[16] O.V. Ogievetsky, A.V. Turbiner, $sl(2,\mathbf R)_q$ and quasi-exactly-solvable problems, Preprint CERN- TH:6212/91, 1991 | MR
[17] I. Cherednik, Teor. Mat. Fys., 61 (1984), 35 | MR | Zbl
[18] E.K. Sklyanin, J. Phys., A21 (1988), 2375 | MR | Zbl
[19] P. Kulishand, N. Reshetikhin, Zap. Nauchn. Semin. LOMI, 101, 1981, 112
[20] E.K. Sklyanin, Func. Anal. Appl., 17 (1983), 273 | DOI | MR | Zbl
[21] V.G. Drinfeld, Dokl. Acad. Nauk, 283 (1985), 1060 | MR | Zbl
[22] M. Jimbo, Lett. Math. Phys., 10 (1985), 63 | DOI | MR | Zbl
[23] N.Yu. Reshetikhin, L.A. Takhtadjan, L.D.Faddeev, Algebra i Analiz, 1:1 (1989), 178 | MR | Zbl
[24] T .Koornwinder, SIAM J. Math. Anal., 24 (1993), 795 | DOI | MR | Zbl
[25] P. Roche, D. Arnaudon, Lett. Math. Phys., 17 (1989), 295 | DOI | MR | Zbl
[26] Func. Anal. Appl., 22 (1988), 170 | DOI | MR | MR
[27] Y. Soibelman, L. Vaksman, Algebra i Analiz, 2:5 (1990), 101 | MR | Zbl
[28] B. Jurco, P. Stovi'cek, Commun. Math. Phys., 152 (1993), 97 | DOI | MR | Zbl
[29] P.P. Kulish, E.K. Sklyanin, Algebraic structures related to reflection equations, Preprint YITP/K-980, 1992 ; P.P. Kulish, “Reflection equation algebras and quantum groups”, Quantum and Noncommutative Analysis, eds. H. Araki et al, Kluwer Academic Publishers, 1993, 207–220 | MR | DOI | MR | Zbl
[30] H.J. de Vega and A. Gonzalez-Ruiz, J. Phys., A26:L519 (1993)
[31] Ya. Granovskii, A. Zhedanov, J. Phys., A26:L357 (1993); Ya. Granovskii, I. Lutzenko and A. Zhedanov, Ann. Phys., 217 (1992), 1 | DOI | MR
[32] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge Univ.Press, 1990 | MR | Zbl
[33] A. Erdelyi et al., Higher Transcendental Functions, Vol.3, Mc Graw-Hill, NY, 1953
[34] L.D. Faddeev and R.M. Kashaev, Generalized Bethe ansatz equations for Hofstadter problem University of Helsinki, preprint HU-TFT-93-63, 1993 | MR
[35] M. Gaudin, La Fonction d'Onde de Bethe, Masson, 1983 | MR | Zbl
[36] V. Bazhanov and Yu. Stroganov, J. Stat. Phys., 59 (1990), 799 | DOI | MR | Zbl
[37] A. Gerasimov, S. Khoroshkin, D. Lebedev, A. Mironov and A. Morozov, Generalized Hirota equations and representation theory. I. The case of $SL(2)$ and $SL_q(2)$, Preprint ITEP M-2/94, FIAN/TD-5/94, NBI-HE-94-27, 1994 | MR
[38] V. Kuznetsov, Teor. Mat. Fys., 91 (1992), 83
[39] Sov. Journ. Nucl. Phys., 7 (1968), 139