6A型顶点算子代数中的Ising向量

The Ising Vectors in 6A-Vertex Operator Algebra

本文主要研究了6A型顶点算子代数中的Ising向量。C. H. Lam,H. Yamada和H. Yamauchi构造了具体的6A型顶点算子代数的例子,计算出了6A型顶点算子代数中有7个Ising向量,并给出了它们之间的关系;S. Sakuma证明了6A型顶点算子代数由两个Ising向量e和f生成的顶点算子代数,并且e和f的内积。但是在后者中只给出了6个Ising向量,第7个Ising向量的具体形式未知。前者构造的具体实例可以看成是后者的一种实现。本文通过两者的Ising向量的对应关系以及6A型顶点算子代数的唯一性,我们求出了第7个Ising向量在一组基下的表达式。

In this paper, we mainly study the Ising vectors in the 6A-algebra. C. H. Lam, H. Yamada and H. Yamauchi constructed an example for the 6A-vertex operator algebra, and they proved that there are seven Ising vectors in the 6A-vertex operator algebra, and they also showed the relations between the Ising vectors. S. Sakuma proved 6A-vertex operator algebra is generated by two Ising vectors e and f, and the inner product of e and f is . But the author only listed six Ising vectors, so we didn’t know the concrete form for the seventh Ising vector. The former can be regarded as a realization of the latter. In this paper, we calculate the seventh Ising vector under a set of bases by the correspondence between them.