Algebraic integrability of Schrodinger operators and representations of Lie algebras
Compositio Mathematica, Volume 98 (1995) no. 1, p. 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},
     publisher = {Kluwer Academic Publishers},
     volume = {98},
     number = {1},
     year = {1995},
     pages = {91-112},
     zbl = {0861.17003},
     mrnumber = {1353287},
     language = {en},
     url = {http://www.numdam.org/item/CM_1995__98_1_91_0}
}
Etingof, Pavel; Styrkas, Konstantin. Algebraic integrability of Schrodinger operators and representations of Lie algebras. Compositio Mathematica, Volume 98 (1995) no. 1, pp. 91-112. http://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. | MR 280103 | Zbl 1002.70558

[Ch] Cherednik, I.: Elliptic quantum many-body problem and double affine Knizhnik-Zamolodchikov equation, preprint; Submitted to Comm. Math. Phys. (1994). | MR 1329203 | Zbl 0826.35100

[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. | MR 1207668 | Zbl 0767.35066

[CV2] Chalykh, O.A. and Veselov, A.P.: Commutative rings of partial differential operators and Lie algebras, Comm. Math. Phys. 126 (1990), 597-611. | MR 1032875 | Zbl 0746.47025

[E] Etingof, P.I.: Quantum integrable systems and representations of Lie algebras, hep-th 9311132, Journal of Mathematical Physics (1993), to appear. | MR 1331279 | Zbl 0861.17002

[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. | MR 1277946 | Zbl 0811.17026

[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 0868.33010

[G] Grinevich, P.G.: Commuting matrix differential operators of arbitrary rank, Soviet Math. Dokl. 30 (1984), no. 2, 515-518. | MR 765610 | Zbl 0598.47049

[HO] Heckman, G.J. and Opdam, E.M.: Root systems and hypergeometric functions I, Compos. Math. 64 (1987), 329-352. | Numdam | MR 918416 | Zbl 0656.17006

[H1] Heckman, G.J.: Root systems and hypergeometric functions II, Compos. Math. 64 (1987), 353-373. | Numdam | MR 918417 | Zbl 0656.17007

[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. | MR 547842 | Zbl 0427.17011

[Kr] Krichever, I.M.: Methods of algebraic geometry in the theory of non-linear equations, Russian Math. Surv. 32:6 (1977), 185-213. | Zbl 0386.35002

[O1] Opdam, E.M.: Root systems and hypergeometric functions III, Compos. Math. 67 (1988), 21-49. | Numdam | MR 949270 | Zbl 0669.33007

[O2] Opdam, E.M.: Root systems and hypergeometric functions IV, Compos. Math. 67 (1988), 191-207. | Numdam | MR 951750 | Zbl 0669.33008

[OOS] Ochiai, H., Oshima, T. and Sekiguchi, H.: Commuting families of symmetric differential operators, (preprint), Univ. of Tokyo (1994). | MR 1272672 | Zbl 0817.22010

[OP] Olshanetsky, M.A. and Perelomov, A.M.: Quantum integrable systems related to Lie algebras, Phys. Rep. 94 (1983), 313-404. | MR 708017 | Zbl 0366.58005

[Osh] Oshima, T.: Completely integrable systems with a symmetry in coordinates, (preprint), Univ. of Tokyo (1994). | MR 1734134 | Zbl 0965.37055

[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 0863.43007

[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 0283.17001

[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. | MR 1221735 | Zbl 0805.47070