W-algebras in lattice vertex operator algebras

本课题的目的是研究与正定偶格相关的顶点算子代数的结构。特别地，我们感兴趣的是由有限阶自同构即一个轨道的不动点组成的子代数。更确切地说，利用根的Coxeter元导出的自同构，研究了√<2>倍于A_2型普通根格的顶点算子代数的轨道。该轨道折叠体包含两个w_3代数作为其子代数，一个中心电荷为4/5，另一个中心电荷为6/5。这两个w_3代数的不可约模的分类是已知的。在已知结果的基础上，我们对轨道折叠进行了详细的研究，并对其不可约模进行了分类。该项目的结果发表在最近的论文中。研究结果也在若干会议和一些国际会议上提出。研究了A_2型的根格。具有一般秩的A型根格的情况应该是一个重要的课题

The purpose of the project is to study the structure of the vertex operator algebras associated with positive definite even lattices. In particular, we are interested in the subalgebra consisting of the fixed points by an automorphism of finite order that is, an orbifold. More precisely, the orbifold of the vertex operator algebra associated with √<2> times an ordinary root lattice of type A_2 by an automorphism induced from the Coxeter element of the root system is studied. The orbifold contains two W_3-algebras as its subalgebras, one is of central charge 4/5 and the other is of central charge 6/5. The classification of irreducible modules for these two W_3-algebras are known. Based on the known results, we have studied the orbifold in detail and classified its irreducible modules. The results obtained in this project are published in recent papers. The results were also presented at several meetings and some international conferences. The work is concerned with the root lattice of type A_2. The case for the root lattice of type A with general rank should be an important subject