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Duke Mathematical Journal

New complex- and quaternion-hyperbolic reflection groups

Daniel Allcock

Source: Duke Math. J. Volume 103, Number 2 (2000), 303-333.

First Page PDF: View first page of article (PDF, 28 KB)

Primary Subjects: 11H06
Secondary Subjects: 11E39, 11F06, 22E40

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1092749438
Mathematical Reviews number (MathSciNet): MR1760630
Digital Object Identifier: doi:10.1215/S0012-7094-00-10326-2
Zentralblatt MATH identifier: 0962.22007

References

D. Allcock, Reflection groups on the octave hyperbolic plane, J. Algebra 213 (1999), 467--498.
Mathematical Reviews (MathSciNet): MR1673465
Digital Object Identifier: doi:10.1006/jabr.1998.7671
--------, The Leech lattice and complex hyperbolic reflections, to appear in Invent. Math.
Mathematical Reviews (MathSciNet): MR1756997
Digital Object Identifier: doi:10.1007/s002220050363
D. Allcock, J. Carlson, and D. Toledo, A complex hyperbolic structure for moduli of cubic surfaces, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), 49--54.
Mathematical Reviews (MathSciNet): MR1649469
Digital Object Identifier: doi:10.1016/S0764-4442(97)82711-5
--------, The complex hyperbolic geometry of the moduli space of cubic surfaces, preprint, 2000.
C. Bachoc, Voisinage au sens de Kneser pour les réseaux quaternioniens, Comment. Math. Helv. 70 (1995), 350--374.
Mathematical Reviews (MathSciNet): MR1340098
Digital Object Identifier: doi:10.1007/BF02566012
C. Bachoc and G. Nebe, Classification of two genera of 32-dimensional lattices of rank 8 over the Hurwitz order, Experiment. Math. 6 (1997), 151--162.
Mathematical Reviews (MathSciNet): MR1474575
Project Euclid: euclid.em/1047650001
R. E. Borcherds, Automorphism groups of Lorentzian lattices, J. Algebra 111 (1987), 133--153.
Mathematical Reviews (MathSciNet): MR913200
Digital Object Identifier: doi:10.1016/0021-8693(87)90245-6
--. --. --. --., Lattices like the Leech lattice, J. Algebra 130 (1990), 219--234.
Mathematical Reviews (MathSciNet): MR1045746
Digital Object Identifier: doi:10.1016/0021-8693(90)90110-A
A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485--535.
Mathematical Reviews (MathSciNet): MR147566
Digital Object Identifier: doi:10.2307/1970210
JSTOR: links.jstor.org
J. H. Conway, The automorphism group of the 26-dimensional even unimodular Lorentzian lattice, J. Algebra 80 (1983), 159--163.
Mathematical Reviews (MathSciNet): MR690711
Digital Object Identifier: doi:10.1016/0021-8693(83)90025-X
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Subgroups, Oxford Univ. Press, Oxford, 1985.
Mathematical Reviews (MathSciNet): MR827219
J. H. Conway, R. A. Parker, and N. J. A. Sloane, The covering radius of the Leech lattice, Proc. Roy. Soc. London Ser. A 380 (1982), 261--290.
Mathematical Reviews (MathSciNet): MR660415
Digital Object Identifier: doi:10.1098/rspa.1982.0042
JSTOR: links.jstor.org
J. H. Conway and N. J. A. Sloane, Laminated lattices, Ann. of Math. (2) 116 (1982), 593--620.
Mathematical Reviews (MathSciNet): MR678483
Digital Object Identifier: doi:10.2307/2007025
JSTOR: links.jstor.org
--. --. --. --., The Coxeter-Todd lattice, the Mitchell group, and related sphere packings, Math. Proc. Cambridge Philos. Soc. 93 (1983), 421--440.
Mathematical Reviews (MathSciNet): MR698347
Digital Object Identifier: doi:10.1017/S0305004100060746
--------, Sphere Packings, Lattices and Groups, Grundlehren Math. Wiss. 290, Springer, New York, 1988.
Mathematical Reviews (MathSciNet): MR920369
H. S. M. Coxeter, ``Factor groups of the braid groups'' in Proceedings of the Fourth Canadian Mathematical Congress (Banff, 1957), Toronto Univ. Press, 1959, 95--122.
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, $4$th ed., Ergeb. Math. Grenzgeb. (3) 14, Springer, Berlin, 1980.
Mathematical Reviews (MathSciNet): MR562913
P. Deligne and G. D. Mostow, Monodromy of hypergeometric functions and nonlattice integral monodromy, Inst. Hautes Études Sci. Publ. Math. 63 (1986), 5--89.
Mathematical Reviews (MathSciNet): MR849651
Digital Object Identifier: doi:10.1007/BF02831622
W. Feit, Some lattices over $Q(\sqrt-3)$, J. Algebra 52 (1978), 248--263.
Mathematical Reviews (MathSciNet): MR498407
Digital Object Identifier: doi:10.1016/0021-8693(78)90273-9
J. Milnor and D. Husemoller, Symmetric Bilinear Forms, Ergeb. Math. Grenzgeb. (3) 73, Springer, New York, 1973.
Mathematical Reviews (MathSciNet): MR506372
G. D. Mostow, On a remarkable class of polyhedra in complex hyperbolic space, Pacific J. Math. 86 (1980), 171--276.
Mathematical Reviews (MathSciNet): MR586876
Project Euclid: euclid.pjm/1102780622
--. --. --. --., Generalized Picard lattices arising from half-integral conditions, Inst. Hautes Études Sci. Publ. Math. 63 (1986), 91--106.
Mathematical Reviews (MathSciNet): MR849652
Digital Object Identifier: doi:10.1007/BF02831623
--. --. --. --., On discontinuous action of monodromy groups on the complex $n$-ball, J. Amer. Math. Soc. 1 (1988), 555--586.
Mathematical Reviews (MathSciNet): MR932662
Digital Object Identifier: doi:10.2307/1990949
JSTOR: links.jstor.org
W. P. Thurston, ``Shapes of polyhedra and triangulations of the sphere'' in The Epstein Birthday Schrift, Geom. Topol. Monogr. 1, Geom. Topol., Coventry, 1998, 511--549. (electronic).
Mathematical Reviews (MathSciNet): MR1668340
Digital Object Identifier: doi:10.2140/gtm.1998.1.511
É. B. Vinberg, The groups of units of certain quadratic forms (in Russian), Mat. Sb. (N.S.) 87 (1972), 18--36.; English translation in Math. USSR-Sb. 87 (1972), 17--35.
Mathematical Reviews (MathSciNet): MR295193
--. --. --. --., On unimodular integral quadratic forms, Funct. Anal. Appl. 6 (1972), 105--111.
Mathematical Reviews (MathSciNet): MR299557
É. B. Vinberg and I. M. Kaplinskaja, On the groups $O_18,1(Z)$ and $O_19,1(Z)$ (in Russian), Dokl. Akad. Nauk SSSR 238 (1978), 1273--1275.; English translation in Soviet Math. Dokl. 19 (1978), 194--197.
Mathematical Reviews (MathSciNet): MR476640

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