The Exceptional Cone and the Leech Lattice

International Mathematics Research Notices

Volumn , Issue 14, 1996, Pages

  Elkies, Noam D ^a   Gross, Benedict H ^a  

^a HARVARD UNIVERSITY   (United States)

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EID: 1842588042     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. A. Ash, D. Mumford, M. Rapoport, and Y.-S. Tai, Smooth Compactification of Locally Symmetric Varieties, Math. Sci. Press, Brookline, Mass., 1975.
2. R. Borcherds, The Leech lattice and other lattices, Ph.D. thesis, Cambridge (Trinity College), 1984.
3. H. Braun and M. Koecher, Jordan-Algebren, Grundlehren Math. Wiss. 128, Springer-Verlag, Berlin, 1966.
4. J. H. Conway, A characterization of Leech's lattice, Invent. Math. 7 (1969), 137-142.
5. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
6. H. S. M. Coxeter, Integral Cayley numbers, Duke Math. J. 13 (1946), 567-578.
7. N. D. Elkies, Mock-laminated lattices, preprint, 1996.
8. H. Freudenthal, Zur ebenen Oktavengeometrie, Proc. Konink. Nederl. Akad. Wetensch. 15 (1953), 195-200.
9. B. H. Gross, A remark on tube domains, Math. Res. Lett. 1 (1994), 1-9.
10. _, Group representations and lattices, J. Amer. Math. Soc. 3 (1990), 929-960.
11. _, Groups over ℤ, Invent. Math. 124 (1996), 263-279.
12. D. W. Hoffmann, On positive definite quadratic forms, Manuscripta Math. 71 (1991), 399-429.
13. N. Jacobson, Some groups of transformations defined by Jordan algebras I, II, III, J. Crelle 201 (1959), 178-195; 204 (1960), 74-98; 207 (1961), 61-85.
14. N. Jacobson, Some groups of transformations defined by Jordan algebras I, II, III, J. Crelle 201 (1959), 178-195; 204 (1960), 74-98; 207 (1961), 61-85.
15. N. Jacobson, Some groups of transformations defined by Jordan algebras I, II, III, J. Crelle 201 (1959), 178-195; 204 (1960), 74-98; 207 (1961), 61-85.
16. C. Jansen, K. Lux, R. Parker, and R. Wilson, An Atlas of Brauer Characters, London Math. Soc. Monographs 11, Clarendon Press, Oxford, 1995.
17. P. Jordan, Nicht-Desarguessche ebene projektive Geometrie, Abh. Math. Sem. Univ. Hamburg 16 (1949), 74-76.
18. P. Jordan, J. von Neumann, and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. of Math. (2) 35 (1934), 29-64.
19. 27, Rev. Mat. Iberoamericana 9 (1993), 139-200.
20. M. Koecher, Jordan algebras and their applications, Univ. of Minn. Lecture Notes, 1962.
21. B. Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. 14 (1986), 207-259.
22. D. Mumford, Abelian Varieties, Tata Inst. Fund. Res. Stud. Math. 5, Oxford Univ. Press, Bombay, 1970.
23. H.-V. Niemeier, Definite quadratische Formen der Dimension 24 und Diskriminante 1, J. Number Theory 5 (1973), 142-178.
24. I. Satake, Algebraic Structures on Symmetric Domains, Kano Memorial Lectures 4, Princeton Univ. Press, Princeton, 1980.
25. J-P. Serre, A Course in Arithmetic, Grad. Texts in Math. 7, Springer-Verlag, New York, 1973.
26. _, "Arithmetic groups" in Homological Group Theory, London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press, Cambridge, 1979, 105-136.
27. T. A. Springer, The projective octave plane I, II, Proc. Kon. Ned. Akad. Wet. A (Iǹdag. Math.) 22 (1960), 74-88, 89-101.
28. A. Weil, Zum Beweis des Torellischen Satzes, Nachr. Akad. Göttingen. Math. Phys. Kl. IIa 1957 (1957), 33-53.