no. 1
Algebraic integrability of Schrodinger operators and representations of Lie algebras
Compositio Mathematica, Tome 98 (1995) no. 1, pp. 91-112 
@article{CM_1995__98_1_91_0,
     author = {Etingof, Pavel and Styrkas, Konstantin},
     title = {Algebraic integrability of {Schrodinger} operators and representations of {Lie} algebras},
     journal = {Compositio Mathematica},
     pages = {91--112},
     year = {1995},
     publisher = {Kluwer Academic Publishers},
     volume = {98},
     number = {1},
     mrnumber = {1353287},
     zbl = {0861.17003},
     language = {en},
     url = {https://www.numdam.org/item/CM_1995__98_1_91_0/}
}
TY  - JOUR
AU  - Etingof, Pavel
AU  - Styrkas, Konstantin
TI  - Algebraic integrability of Schrodinger operators and representations of Lie algebras
JO  - Compositio Mathematica
PY  - 1995
SP  - 91
EP  - 112
VL  - 98
IS  - 1
PB  - Kluwer Academic Publishers
UR  - https://www.numdam.org/item/CM_1995__98_1_91_0/
LA  - en
ID  - CM_1995__98_1_91_0
ER  - 
%0 Journal Article
%A Etingof, Pavel
%A Styrkas, Konstantin
%T Algebraic integrability of Schrodinger operators and representations of Lie algebras
%J Compositio Mathematica
%D 1995
%P 91-112
%V 98
%N 1
%I Kluwer Academic Publishers
%U https://www.numdam.org/item/CM_1995__98_1_91_0/
%G en
%F CM_1995__98_1_91_0
Etingof, Pavel; Styrkas, Konstantin. Algebraic integrability of Schrodinger operators and representations of Lie algebras. Compositio Mathematica, Tome 98 (1995) no. 1, pp. 91-112. https://www.numdam.org/item/CM_1995__98_1_91_0/

[C] Calogero, F.: Solution of the one-dimensional n-body problem with quadratic and/or inversely quadratic pair potentials, J. Math. Phys. 12 (1971), 419-436. | Zbl | MR

[Ch] Cherednik, I.: Elliptic quantum many-body problem and double affine Knizhnik-Zamolodchikov equation, preprint; Submitted to Comm. Math. Phys. (1994). | Zbl | MR

[CV1] Chalykh, O.A. and Veselov, A.P.: Integrability in the theory of Schrödinger operator and harmonic analysis, Comm. Math. Phys. 152 (1993), 29-40. | Zbl | MR

[CV2] Chalykh, O.A. and Veselov, A.P.: Commutative rings of partial differential operators and Lie algebras, Comm. Math. Phys. 126 (1990), 597-611. | Zbl | MR

[E] Etingof, P.I.: Quantum integrable systems and representations of Lie algebras, hep-th 9311132, Journal of Mathematical Physics (1993), to appear. | Zbl | MR

[EK1] Etingof, P.I. and Kirillov Jr., A.A.: Representations of affine Lie algebras, parabolic differential equations, and Lamé functions, hep-th 9310083, Duke Math. J., vol. 74(3), 1994, pages 585-614. | Zbl | MR

[EK2] Etingof, P.I. and Kirillov,, Jr. A.A.: A unified representation-theoretic approach to special functions, hep-th 9312101, Functional Anal. and its Applic. 28 (1994), no. 1. | Zbl

[G] Grinevich, P.G.: Commuting matrix differential operators of arbitrary rank, Soviet Math. Dokl. 30 (1984), no. 2, 515-518. | Zbl | MR

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

[H1] Heckman, G.J.: Root systems and hypergeometric functions II, Compos. Math. 64 (1987), 353-373. | Zbl | MR | Numdam

[KK] Kac, V.G. and Kazhdan, D.A.: Structure of representations with highest weight of infinite dimensional Lie algebras, Advances in Math. 34 (1979), no. 1, 97-108. | Zbl | MR

[Kr] Krichever, I.M.: Methods of algebraic geometry in the theory of non-linear equations, Russian Math. Surv. 32:6 (1977), 185-213. | Zbl

[O1] Opdam, E.M.: Root systems and hypergeometric functions III, Compos. Math. 67 (1988), 21-49. | Zbl | MR | Numdam

[O2] Opdam, E.M.: Root systems and hypergeometric functions IV, Compos. Math. 67 (1988), 191-207. | Zbl | MR | Numdam

[OOS] Ochiai, H., Oshima, T. and Sekiguchi, H.: Commuting families of symmetric differential operators, (preprint), Univ. of Tokyo (1994). | Zbl | MR

[OP] Olshanetsky, M.A. and Perelomov, A.M.: Quantum integrable systems related to Lie algebras, Phys. Rep. 94 (1983), 313-404. | Zbl | MR

[Osh] Oshima, T.: Completely integrable systems with a symmetry in coordinates, (preprint), Univ. of Tokyo (1994). | Zbl | MR

[OS] Oshima, T. and Sekiguchi, H.: Commuting families of differential operators invariant under the action of the Weyl group, (preprint) UTMS 93-43, Dept. of Math. Sci., Univ. of Tokyo (1993). | Zbl

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

[Sh] Shapovalov, N.N.: On bilinear form on the universal enveloping algebra of a simple Lie algebra, Funct. Anal. Appl. 6 (1972), 307-312. | Zbl

[VSC] Veselov, A.P., Styrkas, K.A. and Chalykh, O.A.: Algebraic integrability for the Schrödinger equation and finite reflection groups, Theor. and Math. Physics 94 (1993), no. 2. | Zbl | MR