Mckay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2
Mckay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2
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DOI：
10.1155/imrp.2005.117
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发表时间：
2005-03
期刊：
影响因子：
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通讯作者：
C. Lam;H. Yamada;H. Yamauchi
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文献类型：
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作者：
C. Lam;H. Yamada;H. Yamauchi
本文是(33)的延续，其中构造了格VOA Vp 2E8的几个陪集子代数，并讨论了这些代数与著名的扩展E8图上的McKay观察和Monster单群之间的关系。在本文中，我们将提供技术细节。我们完全确定了所构造的陪集子代数的结构，并证明它们都是由两个中心电荷为1/2的共形向量生成的。我们还研究了这些陪集子代数的表示理论，并表明如果陪集子代数 U 实际上包含在 Moonshine VOA V♮ 中，则两个 Miyamoto 对合的乘积位于 Monster 单群所需的共轭类中。对于 1A、2A、2B 和 4A 的情况，U 在 Moonshine VOA V ♮ 中的存在也成立。此外，还讨论了 3A、5A 和 3C 的情况。并对Monster简单组进行了讨论。在本文中，我们将提供技术细节。我们将确定陪集子代数的结构，并证明它们都是由两个中心电荷为 1/2 的共形向量生成的。我们还研究了这些陪集子代数的表示论，并表明如果陪集子代数 U 实际上包含在 Moonshine 中，则两个 Miyamoto 对合的乘积位于 Monster 单群所需的共轭类中
This paper is a continuation of (33) at which several coset subalgebras of the lattice VOA Vp 2E8 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 article, we shall 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 represen- tation 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 subal- gebra U is actually contained in the Moonshine VOA V ♮ . The existence of U inside the Moonshine VOA V ♮ for the cases of 1A,2A,2B and 4A is also established. Moreover, the cases for 3A, 5A and 3C are discussed. and the Monster simple group were discussed. In this article, we shall provide the technical details. We shall determine the structure of the coset subalgebras 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