No CrossRef data available.
Article contents
An E8 Correspondence for Multiplicative Eta-Products
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We describe an ${{E}_{8}}$ correspondence for the multiplicative eta-products of weight at least 4.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2012
References
[1] Atkin, A. O. L. and Lehner, J., Hecke operators on Γ0
(m). Math. Ann.
185(1970), 134–160. doi:10.1007/BF01359701Google Scholar
[2] Conway, J. H., A simple construction for the Fischer-Griess monster group. Invent. Math.
79(1985), no. 3, 513–540. doi:10.1007/BF01388521Google Scholar
[3] Conway, J. H., Understanding groups like Γ0
(N). In: Groups, Difference Sets, and the Monster. Ohio State Univ. Math. Res. Inst. Publ. 4, de Gruyter, Berlin, 1996, pp. 327–343.Google Scholar
[4] Conway, J. H. and Norton, S. P., Monstrous moonshine. Bull. London Math. Soc.
11(1979), no. 3, 308–339. doi:10.1112/blms/11.3.308Google Scholar
[5] Dummit, D., Kisilevsky, H., and McKay, J., Multiplicative products of η-functions. In: Finite groups—coming of age. Contemp. Math. 45, American Mathematical Society, Providence, RI, 1985, pp. 89–98. See Mathematical Reviews MR822235 (87j:11036) for an important correction of a typesetting error.Google Scholar
[6] Duncan, J. F., Arithmetic groups and the affine E
8
Dynkin diagram. In: Groups and Symmetries. CRM Proc. Lecture Notes 47. American Mathematical Society, Providence, RI, 2009.Google Scholar
[7] Glauberman, G. and Norton, S. P., On McKay's connection between the affine E
8
diagram and the Monster. In: Proceedings on Moonshine and Related Topics. CRM Proc. Lecture Notes 30, American Mathematical Society, Providence, RI, 2001, pp. 37–42.Google Scholar
[8] Helling, H., Bestimmung der Kommensurabilitätsklasse der Hilbertschen Modulgruppe. Math. Z.
92(1966), 269–280. doi:10.1007/BF01112194Google Scholar
[9] Helling, H., On the commensurability class of the rational modular group. J. London Math. Soc.
2(1970), 67–72. doi:10.1112/jlms/s2-2.1.67Google Scholar
[10] Knopp, M. I., Polynomial automorphic forms and nondiscontinuous groups. Trans. Amer. Math. Soc.
123(1966), 506–520. doi:10.1090/S0002-9947-1966-0200447-7Google Scholar
[11] Kondo, T. and Tasaka, T., The theta functions of sublattices of the Leech lattice. Nagoya Math. J.
101(1986), 151–179.Google Scholar
[12] Lam, C. H. and Shimakura, H., Ising vectors in the vertex operator algebra associated with the Leech lattice Λ. Int. Math. Res. Not. IMRN 2007, no. 24.Google Scholar
[13] Lam, C. H., Yamada, H., and Yamauchi, H., McKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2. IMRP Int. Math. Res. Pap.
2005, no. 3, 117–181.Google Scholar
[14] Lam, C. H., Yamada, H., and Yamauchi, H., Vertex operator algebras, extended E
8
diagram, and McKay's observation on the Monster simple group. Trans. Amer. Math. Soc.
359(2007), no. 9, 4107–4123. doi:10.1090/S0002-9947-07-04002-0Google Scholar
[15] McKay, J., Graphs, singularities, and finite groups. In: The Santa Cruz Conference on Finite Groups Proc. Sympos. Pure Math. 37. American Mathematical Society, Providence, RI, pp. 183–186.Google Scholar
[16] Newman, M., Construction and application of a class of modular functions. II. Proc. London Math. Soc.
9(1959), 373–387. doi:10.1112/plms/s3-9.3.373Google Scholar
[17] Siegel, C. L., Some remarks on discontinuous groups. Ann. of Math.
46(1945), 708–718. doi:10.2307/1969206Google Scholar
You have
Access