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A construction of commutative rings of differential operators

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Literature cited

  1. O. A. Chalyth and A. P. Veselov, “Commutative rings of partial differential operators and Lie algebras,” Commun. Math. Phys.,126, 597–611 (1990).

    Google Scholar 

  2. N. Bourbaki, Groupes et algebres de Lie, chs. IV, V et VI, Masson, Paris (1981).

    Google Scholar 

  3. F. Calogero, “Solution of the one-dimensional N-body problem,” J. Math. Phys.,12, 419–436 (1971).

    Google Scholar 

  4. B. Sutherland, “Exact results for a quantum many-body problem in one dimension,” Phys. Rev.,A4, 2019–2021 (1971); Phys. Rev.,A5, 1372–1376 (1972).

    Google Scholar 

  5. M. A. Olshanetsky and A. M. Perelomov, “Quantum completely integrable systems connected with semisimple Lie algebras,” Lett. Math. Phys.,2, 7–13 (1977).

    Google Scholar 

  6. M. A. Ol'shanetskii and A. M. Perelomov, “Quantum systems connected with root systems and the radial parts of Laplace operators,” Funkts. Anal. Prilozhen.,12. No. 2, 57–65 (1978).

    Google Scholar 

  7. G. Heckman and E. Opdam, “Root systems and hypergeometric functions I,” Compositio Math.,64, 329–352 (1987).

    Google Scholar 

  8. G. Heckman, “Root systems and hypergeometric functions II,” Compositio Math.,64, 353–373 (1987).

    Google Scholar 

  9. E. Opdam, “Root systems and hypergeometric functions III,” Compositio Math.,67, 21–49 (1988).

    Google Scholar 

  10. E. Opdam, “Root systems and hypergeometric functions IV,” Compositio Math.,67, 191–209 (1988).

    Google Scholar 

  11. S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York (1962).

    Google Scholar 

  12. S. Helgason, Groups and Geometric Analysis, Academic Press, Orlando (1984).

    Google Scholar 

  13. A. P. Veselov and O. A. Chalykh, “Explicit formulas for spherical functions of type AII symmetric spaces,” Funkts. Anal. Prilozhen.,26, No. 1, 74–76 (1992).

    Google Scholar 

  14. O. A. Chalykh and A. P. Veselov, “Integrability in the theory of Schrödinger operator and harmonic analysis,” Preprint, ETH, Zurich (February, 1992).

    Google Scholar 

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Authors
  1. O. A. Chalykh
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Translated from Matematicheskie Zametki, Vol. 53, No. 3, pp. 121–130, March, 1993.

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Chalykh, O.A. A construction of commutative rings of differential operators. Math Notes 53, 329–335 (1993). https://doi.org/10.1007/BF01207721

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  • DOI: https://doi.org/10.1007/BF01207721

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