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References
[A] Aomoto, K.: Un théorème du typeM−M concernant l'integrale des fonctions multiformes. J. Math. Pures Appl.52, 1–11 (1973)
[BB] Beilinson, A., Bernstein, J.: Localisation ofg-modules II. The Jantzen conjectures. Moscow (Preprint 1989)
[Bj] Bjorner, A.: On the homology of geometric lattices. Algebra Univers.14, No 1, 107–128 (1982)
[Br] Brieskorn, E.: Sur les group des tresses (d'après V.I. Arnold). Séminaire Bourbaki 24e année 1971/72. (Lect. Notes Math., vol. 317) Berlin Heidelberg New York: Springer 1973
[C] Cartier, P.: Les arrangements d'hyperplanes: un chapitre de géométrie combinatoire. Séminaire Bourbaki 33e année 1980/81. (Lect. Notes Math., vol. 901) Berlin Heidelberg New York: Springer 1981
[Ch] Cherednik, I.: Integral solutions of trigonometric Knizhnik-Zamolodchikov equations and Kac-Moody algebras. Moscow (Preprint 1990)
[CF] Christe, P., Flume, R.: The four-point correlations of all primary operators of thed=2 conformally invariant SU(2)o-model with Wess-Zumino term. Nucl. Phys. B282, 466–494 (1987)
[DJMM] Date, E., Jimbo, M., Matsuo, A., Miwa, T.: Hypergeometric-type integrals and the sl(2,C) Knizhnik-Zamolodchikov equation. RIMS-667 (Preprint 1989)
[DF] Dotsenko, Vl.S., Fateev, V.A.: Conformal algebra and multipoint correlation functions in 2D statistical models. Nucl. Phys. N240, 312–348 (1984)
[D] Drinfeld, V.G.: Quantum groups. In: Proceedings of the International Congress of Mathematicians, Berkeley 1986, vol. 1, pp. 798–820. Providence, R.I.: Am. Math. Soc. 1987
[GZ] Gelfand, I.M., Zelevinsky, A.V.: Algebraic and combinatorial aspects of the general theory of hypergeometric functions (in Russian). Funct. Anal. Appl.20, No. 3, 17–34 (1986)
[J] Jantzen, J.C.: Moduln mit einem höchsten Gewicht. (Lect. Notes Math., vol. 75) Berlin Heidelberg New York: Springer 1980
[K] Kac, V.G.: Infinite dimensional Lie algebras. Cambridge: Cambridge University Press 1985
[KZ] Knizhnik, V.G., Zamolodchikov, A.B.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys. B247, 83–103 (1984)
[Ko] Kohno, T.: Quantized universal enveloping algebras and monodromy of braid groups. (Preprint 1988)
[Kos] Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math.74, No. 2, 329–387 (1961)
[L] Lawrence, R.J.: Homology representations of braid groups. Dissertation. Oxford: 1989
[M] Matsuo, A.: An application of Aomoto-Gelfand hypergeometric functions to the SU(n) Knizhnik-Zamolodchikov equation. RIMS-683 (Preprint 1990)
[N] Novikov, S.P.: Bloch homology. Critical points of functions and 1-forms (in Russian). Dokl. Akad. Nauk SSSR287, No. 6, 1321–1424 (1986)
[OS] Orlik, P., Solomon, L.: Combinatorics and topology of complements of hyperplanes. Invent. Math.56, 167–189 (1980)
[SV1] Schechtman, V.V., Varchenko, A.N.: Integral representations ofn-point conformal correlators in the WZW model. MPI/89-51, Bonn (Preprint 1989)
[SV2] Schechtman, V.V., Varchenko, A.N.: Hypergeometric solutions of Knizhnik-Zamolodchikov equations. Lett. Math. Phys.20, 279–283 (1990)
[SV3] Schechtman, V.V., Varchenko, A.N.: Quantum groups and homology of local systems. IAS (Preprint 1990)
[Sh] Shapovalov, N.N.: On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra (in Russian). Funct. Anal. Appl.6, No. 4, 65–70 (1972)
[V] Varchenko, A.N.: Euler Beta-function, Vander Monde determinant. Legendre equation and critical values of linear functions on an arrangement of hyperplanes. I. (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat.53, No. 6, 1206–1235 (1989)
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Oblatum 28-II-1990 & 20-II-1991
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Schechtman, V.V., Varchenko, A.N. Arrangements of hyperplanes and Lie algebra homology. Invent Math 106, 139–194 (1991). https://doi.org/10.1007/BF01243909
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DOI: https://doi.org/10.1007/BF01243909