On classification of parabolic reflection groups in SU (n, 1)

Shoichi KITAGAWA

doi:10.2969/jmsj/04110009

Shoichi KITAGAWA

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 1 Pages 9-36

DOI https://doi.org/10.2969/jmsj/04110009

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Published: 1989 Received: May 19, 1986 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Bourbaki, Groups et Algèbres de Lie, ch. 4,5 et 6, Hermann, Paris, 1968.
2) A. M. Cohen, Finite complex reflection groups, Ann. Sci. École Norm. Sup., 9 (1976), 379-436.
3) H. S. M. Coxeter, Discrete groups generated by reflections, Ann. Math., 35 (1934), 588-621.
4) H. S. M. Coxeter, Finite groups generated by unitary reflections, Abh. Math. Sem. Univ. Hamburg, 31 (1967), 125-135.
5) H. S. M. Coxeter, Regular complex polytopes, Cambridge Univ. Press, 1974.
6) J. Kaneko, S. Tokunaga and M. Yoshida, Complex crystallographic groups II, J. Math. Soc. Japan, 34 (1982), 595-605.
7) I. I. Piatetskii-Shapiro, Automorphic Functions and the Geometry of Classical Domains, Gordon and Breach, New York, 1969.
8) V. L. Popov, Discrete complex reflection groups, Commun. Math. Inst. Rijksuniv. Utrecht, 15 (1982).
9) G. C. Shephard, Unitary groups generated by reflections, Canad. J. Math., 5 (1953), 364-383.
10) G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canad. J. Math., 6 (1954), 274-304.
11) S. Tokunaga and M. Yoshida, Complex crystallographic groups I, J. Math. Soc. Japan, 34 (1982), 581-593.
12) M. Yoshida, Discrete reflection groups in the parabolic subgroup of SU(n, 1) and generalized Cartan matrices of Euclidean type, J. Fac. Sci. Univ. Tokyo, 30 (1983), 25-52.
13) M. Yoshida, Local theory of Fuchsian systems with certain discrete monodromy groups I, Funkcial Ekvac, 21 (1978), 105-137.
14) M. Yoshida and S. Hattori, Local theory of Fuchsian systems with certain discrete monodromy groups III, Funkcial Ekvac, 22 (1979), 1-40.
15) J. A. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1967.

Right : [1] N. Bourbaki, Groups et Algèbres de Lie, ch. 4,5 et 6, Hermann, Paris, 1968.
[2] A. M. Cohen, Finite complex reflection groups, Ann. Sci. École Norm. Sup., 9 (1976), 379-436.
[3] H. S. M. Coxeter, Discrete groups generated by reflections, Ann. Math., 35 (1934), 588-621.
[4] H. S. M. Coxeter, Finite groups generated by unitary reflections, Abh. Math. Sem. Univ. Hamburg, 31 (1967), 125-135.
[5] H. S. M. Coxeter, Regular complex polytopes, Cambridge Univ. Press, 1974.
[6] J. Kaneko, S. Tokunaga and M. Yoshida, Complex crystallographic groups II, J. Math. Soc. Japan, 34 (1982), 595-605.
[7] I. I. Piatetskii-Shapiro, Automorphic Functions and the Geometry of Classical Domains, Gordon and Breach, New York, 1969.
[8] V. L. Popov, Discrete complex reflection groups, Commun. Math. Inst. Rijksuniv. Utrecht, 15 (1982).
[9] G. C. Shephard, Unitary groups generated by reflections, Canad. J. Math., 5 (1953), 364-383.
[10] G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canad. J. Math., 6 (1954), 274-304.
[11] S. Tokunaga and M. Yoshida, Complex crystallographic groups I, J. Math. Soc. Japan, 34 (1982), 581-593.
[12] M. Yoshida, Discrete reflection groups in the parabolic subgroup of SU(n, 1) and generalized Cartan matrices of Euclidean type, J. Fac. Sci. Univ. Tokyo, 30 (1983), 25-52.
[13] M. Yoshida, Local theory of Fuchsian systems with certain discrete monodromy groups I, Funkcial Ekvac, 21 (1978), 105-137.
[14] M. Yoshida and S. Hattori, Local theory of Fuchsian systems with certain discrete monodromy groups III, Funkcial Ekvac, 22 (1979), 1-40.
[15] J. A. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1967.

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