Representation Theory of Code Vertex Operator Algebra
Representation Theory of Code Vertex Operator Algebra
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DOI：
10.1006/jabr.1997.7257
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发表时间：
1998-03
影响因子：
0.9
通讯作者：
M. Miyamoto
中科院分区：
文献类型：
--
作者：
M. Miyamoto
本文研究了由偶二进制线性码构造的码顶点算子代数MD（VOA）的表示理论。我们的主要目的是研究，使用MD的表示理论，VOAV的结构包含一组相互正交的有理共形向量与中心电荷1 - 2，使它们的总和是Virasoro元素的V。这种VOA最著名的例子是Moonshine VOAV。如果一个简单的VOAV包含这样一组共形向量，则V有一个由对合生成的初等阿贝尔自同构2-群P。作为一个P-模，V有一个分解V = π χ ∈ Irr（P）Vχ作为P的权空间V χ的直和.证明了V χ是不可约VP-模.因此，我们可以预期，不可约VP-模的分类及其融合规则将决定V的结构。我们将证明不动点空间VP同构于某个二元线性偶码D的码VOAMD，然后研究和分类所有不可约MD-模，并计算其中一些不可约MD-模的融合规则。
Abstract We study the representation theory of code vertex operator algebrasMD(VOAs) constructed from an even binary linear codeD. Our main purpose is to study, using the representation theory ofMD, the structure of VOAVcontaining a set of mutually orthogonal rational conformal vectors with central charge 1 2 such that the sum of them is the Virasoro element ofV. The most famous example of such VOAs is the Moonshine VOAV♮. If a simple VOAVcontains such a set of conformal vectors, thenVhas an elementary Abelian automorphism 2-groupPgenerated by involutions. As aP-module,Vhas a decompositionV = ⊕ χ ∈ Irr(P)Vχas the direct sum of weight spacesVχofP. It was proved thatVχis an irreducibleVP-module. Therefore, we can expect that the classification of irreducibleVP-modules and their fusion rules will determine the structure ofV. We will show that the fixed point spaceVPis isomorphic to a code VOAMDof some binary linear even codeD, and then study and classify all irreducibleMD-modules and compute the fusion rules of some of them.