Commuting difference operators with polynomial eigenfunctions
Compositio Mathematica, Tome 95 (1995) no. 2, pp. 183-233. 
@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://www.numdam.org/item/CM_1995__95_2_183_0/}
}
TY  - JOUR
AU  - Van Diejen, J. F.
TI  - Commuting difference operators with polynomial eigenfunctions
JO  - Compositio Mathematica
PY  - 1995
SP  - 183
EP  - 233
VL  - 95
IS  - 2
PB  - Kluwer Academic Publishers
UR  - http://www.numdam.org/item/CM_1995__95_2_183_0/
LA  - en
ID  - CM_1995__95_2_183_0
ER  - 
%0 Journal Article
%A Van Diejen, J. F.
%T Commuting difference operators with polynomial eigenfunctions
%J Compositio Mathematica
%D 1995
%P 183-233
%V 95
%N 2
%I Kluwer Academic Publishers
%U http://www.numdam.org/item/CM_1995__95_2_183_0/
%G en
%F 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://www.numdam.org/item/CM_1995__95_2_183_0/

1 Askey, R., Wilson, J.: Some basic hypergeometric orthogonal polynomials. Mem. Amer. Math. Soc. 319 (1985) | Zbl

2 Beerends, R.J., Koomwinder, T.H.: Analysis on root systems: An-1 as limit case of BCn. In preparation | MR

3 Bourbaki, N.: Groupes et algèbres de Lie, Chaps. 4-6. Paris: Hermann 1968 | MR

4 Calogero, F.: 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 Cherednik, I.: Quantum Knizhnik-Zamolodchikov equations and affine root systems. Commun. Math. Phys. 150, 109-136 (1992) | MR | Zbl

6 Cherednik, I.: Double affine Hecke algebras, Knizhnik-Zamolodchikov equations, and Macdonald's operators. Int. Math. Res. Not. no. 9, 171-180 (1992) | MR | Zbl

7 Debiard, A.: Système différentiel hypergéométrique de type BCp. C. R. Acad. Sc. Paris 304 (Série I), 363-366 (1987) | MR | Zbl

8 Debiard, A.: 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 Heckman, G.J., Opdam, E.M.: Root systems and hypergeometric functions I. Compos. Math. 64, 329-352 (1987) | Numdam | MR | Zbl

10 Heckman, G.J.: Root systems and hypergeometric functions II. Compos. Math. 64, 353-373 (1987) | Numdam | MR | Zbl

11 Heckman, G.J.: An elementary approach to the hypergeometric shift operator of Opdam. Invent. Math. 103, 341-350 (1991) | MR | Zbl

12 Inozemtsev, V.I.: Lax representation with spectral parameter on a torus for integrable particle systems. Lett. Math. Phys. 17, 11-17 (1989) | MR | Zbl

13 Koornwinder, T.H.: private notes (1987)

14 Koornwinder, T.H.: Jacobi functions as limit cases of q-ultraspherical polynomials. J. Math. Anal. and Appl. 148, 44-54 (1990) | MR | Zbl

15 Koornwinder, T.H.: 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 Koornwinder, T.H.: 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 Koornwinder, T.H.: Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group. SIAM J. Math. Anal. 24, 795-813 (1993) | MR | Zbl

18 Macdonald, I.G.: Symmetric functions and Hall polynomials. Oxford: Clarendon Press 1979 | MR | Zbl

19 Macdonald, I.G.: 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 Macdonald, I.G.: Orthogonal polynomials associated with root systems. Preprint, Univ. of London (1988) | MR | Zbl

21 Macdonald, I.G.: 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 Macdonald, I.G.: 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 Moser, J.: Three integrable Hamiltonian systems connected with isospectral deformations. Adv. Math. 16, 197-220 (1975) | MR | Zbl

24 Noumi, M.: Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces. To appear in Adv. in Math. | Zbl

25 Opdam, E.M.: Root systems and hypergeometric functions III. Compos. Math. 67, 21-49 (1988) | Numdam | MR | Zbl

26 Opdam, E.M.: Root systems and hypergeometric functions IV. Compos. Math. 67, 191-209 (1988) | Numdam | MR | Zbl

27 Olshanetsky, M.A., Perelomov, A.M.: Classical integrable finite-dimensional systems related to Lie algebras. Phys. Reps. 71, 313-400 (1981) | MR

28 Olshanetsky, M.A., Perelomov, A.M.: Quantum integrable systems related to Lie algebras. Phys. Reps. 94, 313-404 (1983) | MR | Zbl

29 Ruijsenaars, S.N.M., Schneider, H.: A new class of integrable systems and its relation to solitons. Ann. Phys. (N.Y.) 170,370-405 (1986) | MR | Zbl

30 Ruijsenaars, S.N.M.: Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Commun. Math. Phys. 110, 191-213 (1987) | MR | Zbl

31 Ruijsenaars, S.N.M.: Finite-dimensional soliton systems. In.: Kupershmidt, B. (ed.), Integrable and superintegrable systems. pp. 165-206. Singapore: World Scientific 1990 | MR | Zbl

32 Ruijsenaars, S.N.M.: private notes (1993)

33 Sekiguchi, J.: Zonal spherical functions on some symmetric spaces. Publ. RIMS Kyoto Univ. 12 Suppl., 455-459 (1977) | MR | Zbl

34 Serre, J.P.: Complex semisimple Lie algebras. New York: Springer 1987 | MR | Zbl

35 Sutherland, B.: Exact results for a quantum many-body problem in one dimension. Phys. Rev. A4, 2019-2021 (1971)

36 Sutherland, B.: Exact results for a quantum many-body problem in one dimension II. Phys. Rev. A5, 1372-1376 (1972)

37 Van Diejen, J.F.: Integrability of difference Calogero-Moser systems. J. Math. Phys. 35, 2983-3004 (1994) | MR | Zbl

38 Van Diejen, J.F.: Deformations of Calogero-Moser systems and finite Toda chains. To appear in Theoret. and Math. Phys. 99, no. 2 | MR | Zbl

39 Van Diejen, J.F.: Difference Calogero-Moser systems and finite Toda chains. To appear in J. Math. Phys. | MR | Zbl