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The theta functions of sublattices of the Leech lattice

Published online by Cambridge University Press:  22 January 2016

Takeshi Kondo  and
Takashi Tasaka
Takeshi Kondo
Affiliation:
Department of Matheinatics, Colledge of Arts and Sciences University of Tokyo, Komaba, Meguro-ku Tokyo 153, Japan
Takashi Tasaka
Affiliation:
Department of Matheinatics, Colledge of Arts and Sciences University of Tokyo, Komaba, Meguro-ku Tokyo 153, Japan
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Let Λ be the Leech lattice which is an even unimodular lattice with no vectors of squared length 2 in 24-dimensional Euclidean space R24. Then the Mathieu Group M24 is a subgroup of the automorphism group .0 of Λ and the action on Λ of M24 induces a natural permutation representation of M24 on an orthogonal basis For , let Λm be the sublattice of vectors invariant under m:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 101 , March 1986 , pp. 151 - 179
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[1] Conway, J. H., A characterization of Leech’s lattice, Invent. Math., 7 (1969), 137–142.CrossRefGoogle Scholar
[ 2 ] Conway, J. H., Three lectures on exceptional groups, p. 215–247 of Finite Simple Groups, edited by Powell, M. B. and Higman, G., Academic Press, N. Y., 1971.Google Scholar
[ 3 ] Conway, J. H. and Norton, S. P., Monstrous moonshine, Bull, London Math. Soc, 11 (1979), 308–339.CrossRefGoogle Scholar
[4] Koike, M., Mathieu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147–157.Google Scholar
[ 5 ] Shimura, G., Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan, No. 11, Iwanami shoten, Publishers and Princeton University Press, 1971.Google Scholar
[ 6 ] Sloane, N. J. A., Binary Codes, Lattices and sphere packings, p. 117–164 of Cameron, P. J, Combinatorial Surveys, Academic Press, London and New York, 1977.Google Scholar
[ 7 ] Sloane, N. J. A., Codes over GF(4) and complex lattices, J. Algebra, 52 (1978), 168–187.Google Scholar
[ 8 ] Tannery, J. et Molk, J., Elements de la theories des fonctions elliptique, Chelsea, Bronx, New York, 2nd edition, 1972.Google Scholar
[ 9 ] Tasaka, T., On even lattices of 2-square type and self-dual codes, J. Fac. Sci. Univ. Tokyo, 28 (1982), 701–714.Google Scholar
[ 10 ] Thompson, J. G., Finite groups and modular functions, Bull. London Math. Soc, 11 (1979), 347–351.Google Scholar
[ 11 ] Thompson, J. G., Todd, N. J., A representation of the Mathieu group M24 as a collineation group, Ann. Mat. Pure Appl., 71 (1966), 199–238.Google Scholar