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International Mathematics Research Papers (2005) 2005:117-181, doi:10.1155/IMRP.2005.117
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Copyright © 2005 Hindawi Publishing Corporation. All rights reserved.

Mckay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2

Ching Hung Lam, Hiromichi Yamada and Hiroshi Yamauchi

This paper is a continuation of our previous paper in which several coset subalgebras of the lattice VOA Formula were constructed and the relationship between such algebras with the famous McKay observation on the extended E8 diagram and the Monster simple group were discussed. In this paper, we will provide the technical details. We completely determine the structure of the coset subalgebras constructed and show that they are all generated by two conformal vectors of central charge 1/2. We also study the representation theory of these coset subalgebras and show that the product of two Miyamoto involutions is in the desired conjugacy class of the Monster simple group if a coset subalgebra U is actually contained in the Moonshine VOA Formula. The existence of U inside the Moonshine VOA Formula for the cases of 1A, 2abstract, 2B, and 4A is also established. Moreover, the cases for 3A, 5A, and 3X are discussed.


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 Int Math Res NoticesHome page
C. H. Lam and M. Miyamoto
Niemeier lattices, Coxeter elements, and McKay's E8-observation on the Monster simple group
Int Math Res Notices, January 1, 2006; 2006(35967): 35967 - 27.
[Abstract] [PDF]


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