Article PDF
Avoid common mistakes on your manuscript.
Literature Cited
N. Bourbaki, Lie Groups and Algebras [Russian translation], Mir, Moscow (1972).
H. S. M. Coxeter and W. O. J. Moser, Generating Elements and Defining Relations of Discrete Groups [Russian translation], Nauka, Moscow (1980).
V. I. Arnol'd, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Mappings [in Russian], Nauka, Moscow (1982).
V. I. Arnol'd, "Critical points of smooth functions and their normal forms," Usp. Mat. Nauk,30, No. 5, 3–65 (1975).
V. I, Arnol'd, "Critical points of functions on a manifold with boundary, simple Lie groups Bk, Ck, F4, and singularities of evolutes," Usp. Mat. Nauk,33, No. 5, 91–105 (1978).
O. V. Lyashko, "Classification of critical points of functions on a manifold with singular boundary," Funkts. Anal.,17, No. 3, 28–36 (1983).
E. Brieskorn, "Singular elements of semisimple algebraic groups," in: Actes Congres Int. Math., Vol. 2, Nice (1970), pp. 279–284.
Slodowy, "Einfache Singularitaten und einfache algebraische Gruppen," Preprint, Regensburger Mathematische Schriften, 2, Univ. Regensburg (1978).
E. Looijenga, "A period mapping for certain semiuniversal deformations," Compos. Math.,30, No. 3, 299–316 (1975).
S. M. Gusein-Zade, "Monodromy groups of isolated singularities of hypersurfaces," Usp. Mat. Nauk,32, No. 2, 23–65 (1977).
C. T. C. Wall, "A note on symmetry of singularities," Bull. London Math. Soc.,12, No. 3, 169–175 (1980).
C. T. C. Wall, "A second note on symmetry of singularities," Bull. London Math. Soc.,12, No. 5, 347–354 (1980).
G. Wassermann, "Classification of singularities with compact abelian symmetry," Preprint Regensburger Mathematische Schriften, 1, Univ. Regensburg (1977).
J.-P. Serre, Linear Representations of Finite Groups, Springer-Verlag.
T. Springer, Theory of Invariants [Russian translation], Mir, Moscow (1981).
J.-P. Serre, Lie Algebras and Lie Groups, W. A. Benjamin (1965).
A. N. Varchenko, "Asymptotic mixed Hodge structure in vanishing coholomogy," Izv. Akad. Nauk SSSR, Ser. Mat.,45, 540–591 (1981).
A. N. Varchenko and A. B. Givental’, "Period maps and intersection form," Funkts. Anal.,16, No. 2, 7–20 (1982).
B. Malgrange, "Integrals asymptotique et monodromie," Ann. Sci. Ecole Norm. Sup. (4), 405–430 (1974).
J. Steenbrink, "Intersection form for quasihomogeneous singularities," Compos. Math.,34, No. 2, 211–223 (1977).
Additional information
Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 18, No. 3, pp. 1–13, July–September, 1984.
Rights and permissions
About this article
Cite this article
Varchenko, A.N., Chmutov, S.V. Finite irreducible groups, generated by reflections, are monodromy groups of suitable singularities. Funct Anal Its Appl 18, 171–183 (1984). https://doi.org/10.1007/BF01086155
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01086155