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Finite complex reflection groups. (English) Zbl 0359.20029

MSC:
20H15 Other geometric groups, including crystallographic groups
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[1] M. BENARD , Schur Indices and Splitting Fields of the Unitary Reflection Groups , (J. algebra, Vol. 38, 1976 , pp. 318-342). MR 53 #5727 | Zbl 0327.20004 · Zbl 0327.20004 · doi:10.1016/0021-8693(76)90223-4
[2] H. F. BLICHFELDT , The Finite Discontinuous Primitive Groups of Collineations in Four Variables (Math. Ann., Vol. 60, 1905 , pp. 204-231). JFM 36.0214.01 · JFM 36.0214.01
[3] N. BOURBAKI , Groupes et algèbres de Lie , Chap. IV, V, VI, Hermann, Paris, 1968 . Zbl 0186.33001 · Zbl 0186.33001
[4] C. CHEVALLEY , Invariants of Finite Groups Generated by Reflections (Amer. J. Math., Vol. 77, 1955 , pp. 778-782). MR 17,345d | Zbl 0065.26103 · Zbl 0065.26103 · doi:10.2307/2372597
[5] H. S. M. COXETER , Groups Generated by Unitary Reflections of Period Two (Canad J. Math., Vol. 9, 1957 , pp. 243-272). MR 19,248d | Zbl 0077.25101 · Zbl 0077.25101 · doi:10.4153/CJM-1957-032-2
[6] H. S. M. COXETER , Finite Groups Generated by Unitary Reflections (Abh. a. d. Math. Sem. d. Univ., Hamburg, Vol. 31, 1967 , pp. 125-135). MR 37 #6358 | Zbl 0189.32302 · Zbl 0189.32302 · doi:10.1007/BF02992390
[7] C. W. CURTIS and I. REINER , Representation Theory of Finite Groups and Associative Algebras (Intersc. Publ., New York, 1962 . MR 26 #2519 | Zbl 0131.25601 · Zbl 0131.25601
[8] J. DIEUDONNÉ , La géométrie des groupes classiques , Springer-Verlag, Berlin, 1955 , 2nd ed. Zbl 0067.26104 · Zbl 0067.26104
[9] L. DORNHOFF , Group Representation Theory , part A, Marcel Dekker, New York, 1972 . Zbl 0227.20002 · Zbl 0227.20002
[10] P. DU VAL , Homographies, Quaternions and Rotations , Clarendon Press, Oxford, 1964 . MR 29 #6361 | Zbl 0128.15403 · Zbl 0128.15403
[11] W. FEIT , Characters of Finite Groups , Benjamin Publ., New York, 1967 . MR 36 #2715 | Zbl 0166.29002 · Zbl 0166.29002
[12] F. G. FROBENIUS , Gesammelte Abhandelungen , Band III, Springer-Verlag, Berlin, 1968 . Zbl 0169.28901 · Zbl 0169.28901
[13] F. KLEIN , Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade , Teubner, Leipzig, 1884 . Zbl 0803.01037 | JFM 16.0061.01 · Zbl 0803.01037 · eudml:203220
[14] M. KNESER , Über die Ausnahme-Isomorphismen zwischen endlichen klassischen Gruppen (Abh. a. d. Math. Sem. d. Univ., Hamburg, Vol. 31, 1967 , pp. 136-140). MR 38 #5938 | Zbl 0246.20039 · Zbl 0246.20039 · doi:10.1007/BF02992391
[15] J.-P. SERRE , Représentations linéaires des groupes finis , Hermann, Paris, 1967 . MR 38 #1190 | Zbl 0189.02603 · Zbl 0189.02603
[16] G. C. SHEPHARD , Unitary Groups Generated by Reflections (Canad. J. Math., Vol. 5, 1953 , pp. 364-383). MR 14,1060h | Zbl 0052.16403 · Zbl 0052.16403 · doi:10.4153/CJM-1953-042-7
[17] G. C. SHEPHARD and J. A. TODD , Finite Unitary Reflection Groups (Canad. J. Math., Vol. 6, 1954 , pp. 274-304). MR 15,600b | Zbl 0055.14305 · Zbl 0055.14305 · doi:10.4153/CJM-1954-028-3
[18] T. A. SPRINGER , Regular Elements of Finite Reflection Groups (Inv. Math., Vol. 25, 1974 , pp. 159-198). MR 50 #7371 | Zbl 0287.20043 · Zbl 0287.20043 · doi:10.1007/BF01390173 · eudml:142286
[19] R. STEINBERG , Differential Equations Invariant under Finite Reflection Groups (Trans. Amer. Math. Soc., Vol. 112, 1964 , pp. 392-300). MR 29 #4807 | Zbl 0196.39202 · Zbl 0196.39202 · doi:10.2307/1994152
[20] J. A. TODD , The Invariants of a Finite Collineation Group in Five Dimensions (Proc. Cambridge Phil. Soc., Vol. 46, 1950 , pp. 73-90). MR 11,578a | Zbl 0035.09803 · Zbl 0035.09803
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