@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},
year = {1995},
publisher = {Kluwer Academic Publishers},
volume = {95},
number = {2},
mrnumber = {1313873},
zbl = {0838.33010},
language = {en},
url = {https://www.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. https://www.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) | Zbl | MR
5 : Quantum Knizhnik-Zamolodchikov equations and affine root systems. Commun. Math. Phys. 150, 109-136 (1992) | Zbl | MR
6 : Double affine Hecke algebras, Knizhnik-Zamolodchikov equations, and Macdonald's operators. Int. Math. Res. Not. no. 9, 171-180 (1992) | Zbl | MR
7 : Système différentiel hypergéométrique de type BCp. C. R. Acad. Sc. Paris 304 (Série I), 363-366 (1987) | Zbl | MR
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) | Zbl | MR
9 , : Root systems and hypergeometric functions I. Compos. Math. 64, 329-352 (1987) | Zbl | MR | Numdam
10 : Root systems and hypergeometric functions II. Compos. Math. 64, 353-373 (1987) | Zbl | MR | Numdam
11 : An elementary approach to the hypergeometric shift operator of Opdam. Invent. Math. 103, 341-350 (1991) | Zbl | MR
12 : Lax representation with spectral parameter on a torus for integrable particle systems. Lett. Math. Phys. 17, 11-17 (1989) | Zbl | MR
13 : private notes (1987)
14 : Jacobi functions as limit cases of q-ultraspherical polynomials. J. Math. Anal. and Appl. 148, 44-54 (1990) | Zbl | MR
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 | Zbl | MR
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) | Zbl | MR
17 : Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group. SIAM J. Math. Anal. 24, 795-813 (1993) | Zbl | MR
18 : Symmetric functions and Hall polynomials. Oxford: Clarendon Press 1979 | Zbl | MR
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 | Zbl | MR
20 : Orthogonal polynomials associated with root systems. Preprint, Univ. of London (1988) | Zbl | MR
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 | Zbl | MR
23 : Three integrable Hamiltonian systems connected with isospectral deformations. Adv. Math. 16, 197-220 (1975) | Zbl | MR
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) | Zbl | MR | Numdam
26 : Root systems and hypergeometric functions IV. Compos. Math. 67, 191-209 (1988) | Zbl | MR | Numdam
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) | Zbl | MR
29 , : A new class of integrable systems and its relation to solitons. Ann. Phys. (N.Y.) 170,370-405 (1986) | Zbl | MR
30 : Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Commun. Math. Phys. 110, 191-213 (1987) | Zbl | MR
31 : Finite-dimensional soliton systems. In.: Kupershmidt, B. (ed.), Integrable and superintegrable systems. pp. 165-206. Singapore: World Scientific 1990 | Zbl | MR
32 : private notes (1993)
33 : Zonal spherical functions on some symmetric spaces. Publ. RIMS Kyoto Univ. 12 Suppl., 455-459 (1977) | Zbl | MR
34 : Complex semisimple Lie algebras. New York: Springer 1987 | Zbl | MR
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) | Zbl | MR
38 : Deformations of Calogero-Moser systems and finite Toda chains. To appear in Theoret. and Math. Phys. 99, no. 2 | Zbl | MR
39 : Difference Calogero-Moser systems and finite Toda chains. To appear in J. Math. Phys. | Zbl | MR





