Literature Cited
M. Aigner, Combinatorial Theory, Springer-Verlag, New York (1982).
V. I. Arnol'd, "The cohomology ring of the group of dyed braids," Mat. Zametki,5, No. 1, 227–231 (1969).
H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York (1953).
F. A. Berezin and I. M. Gel'fand, "Some remarks on the theory of spherical functions on symmetric Riemann manifolds," Trudy Moskv. Mat. Obshsch.,5, 311–352 (1956).
N. Bourbaki, Lie Groups and Lie Algebras [Russian translation], Mir, Moscow (1972), Chaps. IV–VI.
I. M. Gel'fand, "General theory of hypergeometric functions," Dokl. Akad. Nauk SSSR,288, No. 1, 14–18 (1986).
I. M. Gel'fand and S. I. Gel'fand, "Generalized hypergeometric equations," Dokl. Akad. Nauk SSSR,288, No. 2, 279–283 (1986).
I. M. Gel'fand, S. G. Gindikin, and M. I. Graev, "Integral geometry in affine and projective spaces," Sov. Prob. Mat. (VINITI),16, 53–226 (1980).
I. M. Gel'fand and M. I. Graev, "A duality theorem for general hypergeometric functions," Dokl. Akad. Nauk SSSR,289, No. 1 (1986).
I. M. Gel'fand and A. V. Zelevinskii, "Models for representations of classical groups and their latent symmetries," Funkts. Anal. Prilozhen.,18, No. 3, 14–31 (1984).
B. V. Lidskii, "On the Kostant function of a system of roots An," Funkts. Anal. Prilozhen.,18, No. 1, 76–77 (1984).
Twistors and Gauge Fields [Russian translation], Mir, Moscow (1983).
M. F. Atiyah, "Convexity and commuting Hamiltonians," Bull. London Math. Soc.,14, 1–15 (1982).
A. Bjorner, "On the homology of geometric lattices," Algebra Univ.,14, No. 1, 107–128 (1982).
E. Briskorn, "Sur les groupes de tresses (d'apres V. I. Arnold)," Sém. Bourbaki, 1971/72, Lecture Notes Math., No. 317, Springer-Verlag, New York (1973), pp. 21–44.
P. Cartier, "Les arrangements d'hyperplans; un chapitre de géométrie combinatoire," Sém. Bourbaki, 1980/81, Lecture Notes Math., No. 901, Springer-Verlag, New York (1981), pp. 1–22.
H. Crapo and G. C. Rota, On the Foundations of Combinatorial Theory: Combinatorial Geometries, MIT Press, Cambridge (1970).
J. Folkman, "The homology groups of a lattice," J. Math. Mech.,15, 631–636 (1966).
I. M. Gel'fand and R. MacPherson, "Geometry in Grassmannians and in generalization of the dilogarithm," Adv. Math.,44, No. 3, 279–312 (1982).
V. Guillemin and S. Sternberg, "Convexity properties of the moment mapping," Invent. Math.,67, 491–513 (1982).
B. Kostant, "A formula for the multiplicity of a weight," Trans. Am. Math. Soc.,93, 53–73 (1959).
P. Orlik and L. Solomon, "Combinatorics and topology of complements of hyperplanes," Invent. Math.,56, 167–189 (1980).
D. J. A. Welsh, Matroid Theory, Academic Press, New York (1976).
K. Aomoto, "Les équations aux différences linéaires et les intégrales des fonctions multiformes," J. Fac. Sci. Univ. Tokyo, Math.,22, 271–297 (1975).
K. Aomoto, "Configurations and invariant Gauss—Manin connections of integrals. I," Tokyo J. Math.,5, 249–287 (1982).
Additional information
Moscow State University. Cybernetic Science Society, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 20, No. 3, pp. 17–34, July–September, 1986.
Rights and permissions
About this article
Cite this article
Gel'fand, I.M., Zelevinskii, A.V. Algebraic and combinatorial aspects of the general theory of hypergeometric functions. Funct Anal Its Appl 20, 183–197 (1986). https://doi.org/10.1007/BF01078470
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01078470