Root systems and hypergeometric functions. I

G. J. Heckman; E. M. Opdam

Compositio Mathematica (1987)

  • Volume: 64, Issue: 3, page 329-352
  • ISSN: 0010-437X

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Heckman, G. J., and Opdam, E. M.. "Root systems and hypergeometric functions. I." Compositio Mathematica 64.3 (1987): 329-352. <http://eudml.org/doc/89879>.

@article{Heckman1987,
author = {Heckman, G. J., Opdam, E. M.},
journal = {Compositio Mathematica},
keywords = {Weyl group; root system; hypergeometric functions; hypergeometric (partial) differential equations; monodromy; multivariable hypergeometric functions; commuting differential operators; integrable systems},
language = {eng},
number = {3},
pages = {329-352},
publisher = {Martinus Nijhoff Publishers},
title = {Root systems and hypergeometric functions. I},
url = {http://eudml.org/doc/89879},
volume = {64},
year = {1987},
}

TY - JOUR
AU - Heckman, G. J.
AU - Opdam, E. M.
TI - Root systems and hypergeometric functions. I
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 64
IS - 3
SP - 329
EP - 352
LA - eng
KW - Weyl group; root system; hypergeometric functions; hypergeometric (partial) differential equations; monodromy; multivariable hypergeometric functions; commuting differential operators; integrable systems
UR - http://eudml.org/doc/89879
ER -

References

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  5. [Del 1] P. Deligne, Equations Différentielles à Points Singuliers Reguliers, LNM 163, Springer-Verlag (1970). Zbl0244.14004MR417174
  6. [Del 2] P. Deligne, Les immeubles des groupes de tresses généralisés, Inv. Math.17 (1972) 273-302. Zbl0238.20034MR422673
  7. [Er] A. Erdélyi, Higher Transcendental Functions I, R.E. Kneger Publ. Co. (1981). 
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  9. [Ha] Harish-Chandra, Spherical functions on a semisimple Lie group I, Amer. J. Math80 (1958) 241-310. Zbl0093.12801MR94407
  10. [Hec 1] G.J. Heckman, The Calogero system and finite reflection groups, unpublished manuscript (1984). 
  11. [Hec 2] G.J. Heckman, Root Systems and Hypergeometric Functions II, preprint (1986). Zbl0656.17007
  12. [Hel 1] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Acad. Press (1978). Zbl0451.53038MR514561
  13. [Hel 2] S. Helgason, Groups and Geometric Analysis, Acad. Press (1984). Zbl0543.58001MR754767
  14. [K] T.H. Koornwinder, Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators I-IV, Indag. Math36. (1974) 48-66 and 358-381. MR340673
  15. [vdL] H. v.d. Lek, The Homotopy Type of Complex Hyperplane Complements, Thesis, Nijmegen (1983). 
  16. [Mac] I.G. Macdonald, unpublished manuscript (1985). 
  17. [Mal] B. Malgrange, Regular Connections after Deligne, manuscript (1985). 
  18. [Mo] J. Moser, Three integrable Hamiltonian systems Connected with isospectral deformations, Adv. in Math.16 (1975) 197-220. Zbl0303.34019MR375869
  19. [Ng] Nguyên Viêt Dung.The fundamental groups of the spaces of regular orbits of the affine Weyl groups, Topology22 (1983) 425-435. Zbl0524.57015MR715248
  20. [Op] E.M. Opdam, Root Systems and Hypergeometric Functions III, preprint (1986). 
  21. [OP] M.A. Olshanetsky and A.M. Perelomov, Completely integrable Hamiltonian systems associated with semisimple Lie algebras, Inv. Math.37 (1976) 93-108. Zbl0342.58017MR426053
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Citations in EuDML Documents

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  1. E. M. Opdam, Root systems and hypergeometric functions III
  2. G. J. Heckman, Root systems and hypergeometric functions. II
  3. E. M. Opdam, Root systems and hypergeometric functions IV
  4. Pavel Etingof, Konstantin Styrkas, Algebraic integrability of Schrodinger operators and representations of Lie algebras
  5. R. J. Beerends, The Abel transform and shift operators
  6. J. F. Van Diejen, Commuting difference operators with polynomial eigenfunctions
  7. G. C. M. Ruitenburg, Invariant ideals of polynomial algebras with multiplicity free group action
  8. I. G. MacDonald, Affine Hecke algebras and orthogonal polynomials
  9. E. M. Opdam, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group
  10. G. J. Heckman, Dunkl operators

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