@article{CM_1995__95_2_183_0, author = {Van Diejen, J. F.}, title = {Commuting difference operators with polynomial eigenfunctions}, journal = {Compositio Mathematica}, pages = {183--233}, publisher = {Kluwer Academic Publishers}, volume = {95}, number = {2}, year = {1995}, mrnumber = {1313873}, zbl = {0838.33010}, language = {en}, url = {http://archive.numdam.org/item/CM_1995__95_2_183_0/} }
Van Diejen, J. F. Commuting difference operators with polynomial eigenfunctions. Compositio Mathematica, Tome 95 (1995) no. 2, pp. 183-233. http://archive.numdam.org/item/CM_1995__95_2_183_0/
1 Some basic hypergeometric orthogonal polynomials. Mem. Amer. Math. Soc. 319 (1985) | Zbl
, :2 Analysis on root systems: An-1 as limit case of BCn. In preparation | MR
, :3 Groupes et algèbres de Lie, Chaps. 4-6. Paris: Hermann 1968 | MR
:4 Solutions of the one-dimensional n-body problems with quadratic and/or inversely quadratic pair potentials. J. Math. Phys. 12, 419-436 (1971) | MR | Zbl
:5 Quantum Knizhnik-Zamolodchikov equations and affine root systems. Commun. Math. Phys. 150, 109-136 (1992) | MR | Zbl
:6 Double affine Hecke algebras, Knizhnik-Zamolodchikov equations, and Macdonald's operators. Int. Math. Res. Not. no. 9, 171-180 (1992) | MR | Zbl
:7 Système différentiel hypergéométrique de type BCp. C. R. Acad. Sc. Paris 304 (Série I), 363-366 (1987) | MR | Zbl
:8 Parties radiales des opérateurs invariants des espaces symétriques de type BCp: intégrales premières d'un hamiltonien à symétrie BCp. C. R. Acad. Sc. Paris 304 (Série I), 415-417 (1987) | MR | Zbl
:9 Root systems and hypergeometric functions I. Compos. Math. 64, 329-352 (1987) | Numdam | MR | Zbl
, :10 Root systems and hypergeometric functions II. Compos. Math. 64, 353-373 (1987) | Numdam | MR | Zbl
:11 An elementary approach to the hypergeometric shift operator of Opdam. Invent. Math. 103, 341-350 (1991) | MR | Zbl
:12 Lax representation with spectral parameter on a torus for integrable particle systems. Lett. Math. Phys. 17, 11-17 (1989) | MR | Zbl
:13 private notes (1987)
:14 Jacobi functions as limit cases of q-ultraspherical polynomials. J. Math. Anal. and Appl. 148, 44-54 (1990) | MR | Zbl
:15 Orthogonal polynomials in connection with quantum groups. In: Nevai, P. (ed.), Orthogonal polynomials: theory and practice. NATO ASI Series C 294, pp. 257-292. Dordrecht: Kluwer Academic Publishers 1990 | MR | Zbl
:16 Askey-Wilson polynomials for root systems of type BC. In: Richards, D. St. P. (ed.), Hypergeometric functions on domains of positivity, Jack polynomials, and applications. Contemp. Math. 138, pp. 189-204 (1992) | MR | Zbl
:17 Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group. SIAM J. Math. Anal. 24, 795-813 (1993) | MR | Zbl
:18 Symmetric functions and Hall polynomials. Oxford: Clarendon Press 1979 | MR | Zbl
:19 Commuting differential operators and zonal spherical functions. In: Cohen, A. M., e. a. (eds.), Algebraic groups Utrecht 1986. Lect. Notes in Math. 1271, pp. 189-200. Berlin: Springer 1987 | MR | Zbl
:20 Orthogonal polynomials associated with root systems. Preprint, Univ. of London (1988) | MR | Zbl
:21 A new class of symmetric functions. In: Cerlienco, L., Foata, D. (eds.), Actes 20e Séminaire Lotharingien Combinatoire, pp. 131-171. Strasbourg: Publ. I. R. M. A. 1988 | Zbl
:22 Orthogonal polynomials associated with root systems. In: Nevai, P. (ed.), Orthogonal polynomials: theory and practice. NATO ASI Series C 294, pp. 311-318. Dordrecht: Kluwer Academic Publishers 1990 | MR | Zbl
:23 Three integrable Hamiltonian systems connected with isospectral deformations. Adv. Math. 16, 197-220 (1975) | MR | Zbl
:24 Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces. To appear in Adv. in Math. | Zbl
:25 Root systems and hypergeometric functions III. Compos. Math. 67, 21-49 (1988) | Numdam | MR | Zbl
:26 Root systems and hypergeometric functions IV. Compos. Math. 67, 191-209 (1988) | Numdam | MR | Zbl
:27 Classical integrable finite-dimensional systems related to Lie algebras. Phys. Reps. 71, 313-400 (1981) | MR
, :28 Quantum integrable systems related to Lie algebras. Phys. Reps. 94, 313-404 (1983) | MR | Zbl
, :29 A new class of integrable systems and its relation to solitons. Ann. Phys. (N.Y.) 170,370-405 (1986) | MR | Zbl
, :30 Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Commun. Math. Phys. 110, 191-213 (1987) | MR | Zbl
:31 Finite-dimensional soliton systems. In.: Kupershmidt, B. (ed.), Integrable and superintegrable systems. pp. 165-206. Singapore: World Scientific 1990 | MR | Zbl
:32 private notes (1993)
:33 Zonal spherical functions on some symmetric spaces. Publ. RIMS Kyoto Univ. 12 Suppl., 455-459 (1977) | MR | Zbl
:34 Complex semisimple Lie algebras. New York: Springer 1987 | MR | Zbl
:35 Exact results for a quantum many-body problem in one dimension. Phys. Rev. A4, 2019-2021 (1971)
:36 Exact results for a quantum many-body problem in one dimension II. Phys. Rev. A5, 1372-1376 (1972)
:37 Integrability of difference Calogero-Moser systems. J. Math. Phys. 35, 2983-3004 (1994) | MR | Zbl
:38 Deformations of Calogero-Moser systems and finite Toda chains. To appear in Theoret. and Math. Phys. 99, no. 2 | MR | Zbl
:39 Difference Calogero-Moser systems and finite Toda chains. To appear in J. Math. Phys. | MR | Zbl
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