메뉴 건너뛰기




Volumn 330, Issue 1-3, 2001, Pages 149-203

Two linear transformations each tridiagonal with respect to an eigenbasis of the other

Author keywords

05E30; 05E35; 33C45; 33D45; Askey scheme; Askey Wilson algebra; Dolan Grady relations; Q Racah polynomial; Quadratic algebra; Serre relations; Subconstituent algebra; Terwilliger algebra

Indexed keywords


EID: 0035877109     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00242-7     Document Type: Article
Times cited : (269)

References (40)
  • 1
    • 0012649765 scopus 로고
    • Onsager algebra and integrable lattice models
    • Ahn C., Shigemoto K. Onsager algebra and integrable lattice models. Modern Phys. Lett. A. 6(38):1991;3509-3515.
    • (1991) Modern Phys. Lett. a , vol.6 , Issue.38 , pp. 3509-3515
    • Ahn, C.1    Shigemoto, K.2
  • 2
    • 0001066491 scopus 로고
    • A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols
    • Askey R., Wilson J. A set of orthogonal polynomials that generalize the Racah coefficients or. 6-j symbols SIAM J. Math. Anal. 10(5):1979;1008-1016.
    • (1979) SIAM J. Math. Anal. , vol.10 , Issue.5 , pp. 1008-1016
    • Askey, R.1    Wilson, J.2
  • 3
    • 0001308382 scopus 로고
    • Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
    • Askey R., Wilson J. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Am. Math. Soc. 54(319):1985;iv + 55.
    • (1985) Mem. Am. Math. Soc. , vol.54 , Issue.319 , pp. 55
    • Askey, R.1    Wilson, J.2
  • 7
    • 0001797280 scopus 로고    scopus 로고
    • The Terwilliger algebras of bipartite P- and Q-polynomial schemes
    • Caughman IV J.S. The Terwilliger algebras of bipartite P- and Q-polynomial schemes. Discrete Math. 196(1-3):1999;65-95.
    • (1999) Discrete Math. , vol.196 , Issue.13 , pp. 65-95
    • Caughman IV, J.S.1
  • 8
    • 0007109637 scopus 로고
    • Quantum affine algebras
    • Chari V., Pressley A. Quantum affine algebras. Comm. Math. Phys. 142(2):1991;261-283.
    • (1991) Comm. Math. Phys. , vol.142 , Issue.2 , pp. 261-283
    • Chari, V.1    Pressley, A.2
  • 9
    • 0002978237 scopus 로고
    • Quantum affine algebras and their representations
    • in: (Banff, AB, 1994), AMS, Providence, RI
    • V. Chari, A. Pressley, Quantum affine algebras and their representations, in: Representations of Groups (Banff, AB, 1994), AMS, Providence, RI, 1995, pp. 59-78.
    • (1995) Representations of Groups , pp. 59-78
    • Chari, V.1    Pressley, A.2
  • 10
    • 0001773804 scopus 로고    scopus 로고
    • The girth of a thin distance-regular graph
    • Collins B.V.C. The girth of a thin distance-regular graph. Graphs Combin. 13(1):1997;21-30.
    • (1997) Graphs Combin. , vol.13 , Issue.1 , pp. 21-30
    • Collins, B.V.C.1
  • 11
    • 0000225796 scopus 로고    scopus 로고
    • Bipartite distance-regular graphs. I
    • Curtin B. Bipartite distance-regular graphs. I. Graphs Combin. 15(2):1999;143-158.
    • (1999) Graphs Combin. , vol.15 , Issue.2 , pp. 143-158
    • Curtin, B.1
  • 12
    • 0347851585 scopus 로고    scopus 로고
    • Bipartite distance-regular graphs. II
    • Curtin B. Bipartite distance-regular graphs. II. Graphs Combin. 15(4):1999;377-391.
    • (1999) Graphs Combin. , vol.15 , Issue.4 , pp. 377-391
    • Curtin, B.1
  • 13
    • 0000800502 scopus 로고    scopus 로고
    • Distance-regular graphs which support a spin model are thin
    • in: The 16th British Combinatorial Conference, London
    • B. Curtin, Distance-regular graphs which support a spin model are thin, in: The 16th British Combinatorial Conference, London, 1997, Discrete Math. 197/198 (1999) 205-216.
    • (1997) Discrete Math. , vol.197-198 , pp. 205-216
    • Curtin, B.1
  • 15
    • 0004016031 scopus 로고
    • Wiley, New York, (With Applications to Finite Groups and Orders, Reprint of the original, Wiley/Interscience, New York)
    • C.W. Curtis, I. Reiner, Methods of Representation Theory, vol. I, Wiley, New York, 1990 (With Applications to Finite Groups and Orders, Reprint of the 1981 original, Wiley/Interscience, New York).
    • (1981) Methods of Representation Theory , vol.1
    • Curtis, C.W.1    Reiner, I.2
  • 16
    • 0001592752 scopus 로고
    • Onsager's algebra and superintegrability
    • Davies B. Onsager's algebra and superintegrability. J. Phys. A. 23(12):1990;2245-2261.
    • (1990) J. Phys. a , vol.23 , Issue.12 , pp. 2245-2261
    • Davies, B.1
  • 17
    • 0000152761 scopus 로고
    • Onsager's algebra and the Dolan-Grady condition in the non-self-dual case
    • Davies B. Onsager's algebra and the Dolan-Grady condition in the non-self-dual case. J. Math. Phys. 32(11):1991;2945-2950.
    • (1991) J. Math. Phys. , vol.32 , Issue.11 , pp. 2945-2950
    • Davies, B.1
  • 18
    • 0000426640 scopus 로고
    • Conserved charges from self-duality
    • Dolan L., Grady M. Conserved charges from self-duality. Phys. Rev. D (3). 25(6):1982;1587-1604.
    • (1982) Phys. Rev. D (3) , vol.25 , Issue.6 , pp. 1587-1604
    • Dolan, L.1    Grady, M.2
  • 21
    • 21144467942 scopus 로고
    • Spherical q-functions
    • Granovski i Y.I., Zhedanov A.S. Spherical q-functions. J. Phys. A. 26(17):1993;4331-4338.
    • (1993) J. Phys. a , vol.26 , Issue.17 , pp. 4331-4338
    • Granovskii, Y.I.1    Zhedanov, A.S.2
  • 22
    • 22244440285 scopus 로고
    • Mutual integrability, quadratic algebras, and dynamical symmetry
    • Granovski i Ya.I., Lutzenko I.M., Zhedanov A.S. Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217(1):1992;1-20.
    • (1992) Ann. Phys. , vol.217 , Issue.1 , pp. 1-20
    • Granovskii, Ya.I.1    Lutzenko, I.M.2    Zhedanov, A.S.3
  • 25
    • 0011295507 scopus 로고    scopus 로고
    • The structure of nonthin irreducible T-modules of endpoint. 1: Ladder bases and classical parameters
    • Hobart S., Ito T. The structure of nonthin irreducible T-modules of endpoint. 1: Ladder bases and classical parameters. J. Algebraic Combin. 7(1):1998;53-75.
    • (1998) J. Algebraic Combin. , vol.7 , Issue.1 , pp. 53-75
    • Hobart, S.1    Ito, T.2
  • 27
    • 0003176060 scopus 로고
    • Group theoretic interpretations of Askey's scheme of hypergeometric orthogonal polynomials
    • in: Orthogonal Polynomials and Their Applications (Segovia, Springer, Berlin
    • T.H. Koornwinder, Group theoretic interpretations of Askey's scheme of hypergeometric orthogonal polynomials, in: Orthogonal Polynomials and Their Applications (Segovia, 1986), Lecture Notes in Mathematics, vol. 1329, Springer, Berlin, 1988, pp. 46-72.
    • (1986) Lecture Notes in Mathematics , vol.1329 , pp. 46-72
    • Koornwinder, T.H.1
  • 28
    • 0001282924 scopus 로고
    • Orthogonal polynomials duality, and association schemes
    • Leonard D.A. Orthogonal polynomials duality, and association schemes. SIAM J. Math. Anal. 13(4):1982;656-663.
    • (1982) SIAM J. Math. Anal. , vol.13 , Issue.4 , pp. 656-663
    • Leonard, D.A.1
  • 29
    • 0011345206 scopus 로고
    • Parameters of association schemes that are both P- and Q-polynomial
    • Leonard D.A. Parameters of association schemes that are both P- and Q-polynomial. J. Combin. Theory Ser. A. 36(3):1984;355-363.
    • (1984) J. Combin. Theory Ser. a , vol.36 , Issue.3 , pp. 355-363
    • Leonard, D.A.1
  • 30
    • 0011494817 scopus 로고
    • Star-triangle equations, quantum Lax pairs, and higher genus curves
    • in: (Brunswick, ME, AMS, Providence, RI
    • J.H.H. Perk, Star-triangle equations, quantum Lax pairs, and higher genus curves, in: Theta Functions - Bowdoin 1987, Part 1 (Brunswick, ME, 1987), AMS, Providence, RI, 1989, pp. 341-354.
    • (1987) Theta Functions - Bowdoin 1987 , Issue.1 PART , pp. 341-354
    • Perk, J.H.H.1
  • 31
    • 0000203819 scopus 로고    scopus 로고
    • The irreducible modules of the Terwilliger algebras of Doob schemes
    • Tanabe K. The irreducible modules of the Terwilliger algebras of Doob schemes. J. Algebraic Combin. 6(2):1997;173-195.
    • (1997) J. Algebraic Combin. , vol.6 , Issue.2 , pp. 173-195
    • Tanabe, K.1
  • 32
    • 38249035194 scopus 로고
    • A characterization of P- and Q-polynomial association schemes
    • Terwilliger P. A characterization of P- and Q-polynomial association schemes. J. Combin. Theory Ser. A. 45(1):1987;8-26.
    • (1987) J. Combin. Theory Ser. a , vol.45 , Issue.1 , pp. 8-26
    • Terwilliger, P.1
  • 33
    • 0000745775 scopus 로고
    • The subconstituent algebra of an association scheme. I
    • Terwilliger P. The subconstituent algebra of an association scheme. I. J. Algebraic Combin. 1(4):1992;363-388.
    • (1992) J. Algebraic Combin. , vol.1 , Issue.4 , pp. 363-388
    • Terwilliger, P.1
  • 34
    • 0002641888 scopus 로고
    • The subconstituent algebra of an association scheme. II
    • Terwilliger P. The subconstituent algebra of an association scheme. II. J. Algebraic Combin. 2(1):1993;73-103.
    • (1993) J. Algebraic Combin. , vol.2 , Issue.1 , pp. 73-103
    • Terwilliger, P.1
  • 35
    • 84951517865 scopus 로고
    • The subconstituent algebra of an association scheme. III
    • Terwilliger P. The subconstituent algebra of an association scheme. III. J. Algebraic Combin. 2(2):1993;177-210.
    • (1993) J. Algebraic Combin. , vol.2 , Issue.2 , pp. 177-210
    • Terwilliger, P.1
  • 36
    • 0001466378 scopus 로고
    • A new inequality for distance-regular graphs
    • Terwilliger P. A new inequality for distance-regular graphs. Discrete Math. 137(1-3):1995;319-332.
    • (1995) Discrete Math. , vol.137 , Issue.13 , pp. 319-332
    • Terwilliger, P.1
  • 37
    • 0030545655 scopus 로고    scopus 로고
    • Sl(N) Onsager's algebra and integrability
    • Uglov D.B., Ivanov I.T. sl(N) Onsager's algebra and integrability J. Statist. Phys. 82(1-2):1996;87-113.
    • (1996) J. Statist. Phys. , vol.82 , Issue.12 , pp. 87-113
    • Uglov, D.B.1    Ivanov, I.T.2
  • 38
    • 1542755349 scopus 로고
    • Hidden symmetry of Askey-Wilson polynomials
    • Zhedanov A.S. Hidden symmetry of Askey-Wilson polynomials. Teoret. Mat. Fiz. 89(2):1991;190-204.
    • (1991) Teoret. Mat. Fiz. , vol.89 , Issue.2 , pp. 190-204
    • Zhedanov, A.S.1
  • 39
    • 0000047342 scopus 로고
    • q(2) algebra: Cartesian version and overlaps
    • q(2) algebra: Cartesian version and overlaps Modern Phys. Lett. A. 7(18):1992;1589-1593.
    • (1992) Modern Phys. Lett. a , vol.7 , Issue.18 , pp. 1589-1593
    • Zhedanov, A.S.1
  • 40
    • 21144479738 scopus 로고
    • Hidden symmetry algebra and overlap coefficients for two ring-shaped potentials
    • Zhedanov A.S. Hidden symmetry algebra and overlap coefficients for two ring-shaped potentials. J. Phys. A. 26(18):1993;4633-4641.
    • (1993) J. Phys. a , vol.26 , Issue.18 , pp. 4633-4641
    • Zhedanov, A.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.