@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}, publisher = {Kluwer Academic Publishers}, volume = {98}, number = {1}, year = {1995}, zbl = {0861.17003}, mrnumber = {1353287}, language = {en}, url = {http://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 - http://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 http://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, Volume 98 (1995) no. 1, pp. 91-112. http://www.numdam.org/item/CM_1995__98_1_91_0/

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

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

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

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

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

:[EK1] 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 | Zbl

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

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

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

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

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

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

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

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

:[OOS] Commuting families of symmetric differential operators, (preprint), Univ. of Tokyo (1994). | MR | Zbl

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

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

:[OS] 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

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

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

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

, and :