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On the discrete groups of Moonshine
Author(s):
John
Conway;
John
McKay;
Abdellah
Sebbar
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2233-2240.
MSC (2000):
Primary 11F22, 11F03;
Secondary 30F35, 20C34
Posted:
March 25, 2004
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Abstract:
We characterize the 171 discrete subgroups of occurring in Monstrous Moonshine in terms of their group-theoretic properties alone.
References:
-
- 1.
- M. Akbas and D. Singerman, The signature of the normalizer of
. Groups, Combinatorics and Geometry (Durham, 1990), 77-86, London Math. Soc. Lecture Note Ser., 165, Cambridge University Press, Cambridge, 1992. MR 94a:20081 - 2.
- B. J. Birch and W. Kuyk, eds., Modular functions of one variable IV, Proc. Internat. Summer School (Antwerp, 1972), Lecture Notes in Mathematics, no. 476, Springer-Verlag, New York, 1975. MR 51:12708
- 3.
- R. Borcherds, Monstrous Moonshine and Monstrous Lie superalgebras, Invent. Math. 109 (1992), 405-444. MR 94f:11030
- 4.
- R. Borcherds, Automorphic forms on
and infinite products, Invent. Math. 120 (1995), 161-213. MR 96j:11067 - 5.
- J. H. Conway, Understanding groups like
. Groups, Difference Sets, and the Monster (Columbus, OH, 1993), 327-343, Ohio State Univ. Math. Res. Inst. Publ., 4, de Gruyter, Berlin, 1996. MR 98b:11041 - 6.
- J. H. Conway, The orbifold notation for surface groups. Groups, Combinatorics and Geometry (Durham, 1990), 438-447, London Math. Soc. Lecture Note Ser., 165, Cambridge University Press, Cambridge, 1992. MR 94a:57025
- 7.
- J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. London Math. Soc. 11 (1979), 308-339. MR 81j:20028
- 8.
- C. Dong, H. Li, and G. Mason, Modular-invariance of trace functions in orbifold theory and generalised Moonshine, Commun. Math. Phys. 214 (2000), 1-56. MR 2001k:17043
- 9.
- C. Dong and G. Mason, An orbifold theory of genus zero associated to the sporadic group
, Comm. Math. Phys. 164 (1994), no. 1, 87-104. MR 96a:11041 - 10.
- C. Ferenbaugh, On the modular functions involved in ``Monstrous Moonshine'', Ph.D. dissertation, Princeton University, 1992.
- 11.
- I. Frenkel, J. Lepowsky, and A. Meurman, Vertex operator algebras and the Monster, Pure and Applied Mathematics, vol. 134, Academic Press, Inc., Boston, MA, 1988. MR 90h:17026
- 12.
- D. Ford, J. McKay and S. Norton, More on replicable functions, Comm. Algebra 22 (1994), 5175-5193. MR 95i:11036
- 13.
- R. Fricke, Die elliptische Funktionen und ihre Anwendungen, 2-ter Teil (Teubner, Leipzig, 1892).
- 14.
- R. Griess, The friendly giant, Invent. Math. 69 (1982), 1-102. MR 84m:20024
- 15.
- J. Harvey and G. Moore, Algebras, BPS states, and strings, Nucl. Phys. B463 (1996) 315-368. MR 97h:81163
- 16.
- Y.-Z. Huang, Two-dimensional conformal geometry and vertex operator algebras, Progress in Mathematics, 148, Birkhäuser Boston, Inc., Boston, MA, 1997. MR 98i:17037
- 17.
- R. Ivanov and M. Tuite, Rational generalised Moonshine from Abelian orbifoldings of the Moonshine module, Nucl. Phys. B635 (2002), 435-472. MR 2003g:11040
- 18.
- P. G. Kluit, On the normalizer of
, in Modular Functions of One Variable, V (Bonn, 1976), 239-246, Lecture Notes in Mathematics, no. 601, Springer-Verlag, New York, 1977. MR 58:513 - 19.
- A. P. Ogg, Automorphismes des courbes modulaires, Séminaire Delange-Pisot, Poitou, (7), 1974.
- 20.
- M. Tuite, Monstrous Moonshine from orbifolds, Comm. Math. Phys. 146 (1992), no. 2, 277-309. MR 93f:11036
- 21.
- M. Tuite, On the relationship between Monstrous Moonshine and the uniqueness of the Moonshine Module, Commun. Math. Phys. 166 (1995), 495-532. MR 96b:17027
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Additional Information:
John
Conway
Affiliation:
Department of Mathematics, Fine Hall, Princeton University, Washington Road, Princeton, New Jersey 08544-1000
Email:
conway@math.princeton.edu
John
McKay
Affiliation:
Department of Mathematics and CICMA, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada
Email:
mckay@cs.concordia.ca
Abdellah
Sebbar
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
Email:
sebbar@mathstat.uottawa.ca
DOI:
10.1090/S0002-9939-04-07421-0
PII:
S 0002-9939(04)07421-0
Keywords:
Monster,
Moonshine,
discrete groups,
principal moduli
Received by editor(s):
August 2, 2002
Received by editor(s) in revised form:
May 7, 2003
Posted:
March 25, 2004
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2004,
American Mathematical Society
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