Vertex operator algebras with group action

具有群作用的顶点算子代数

• 批准号: 09640019
• 负责人: YAMADA Hiromichi
• 金额: $ 1.09万
• 依托单位: Hitotsubashi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640019/
• 关键词: vertex operator algebra; Virasoro algebra; conformal element; finite group; simple module

In 1997 a subalgebra having order three symmetry of a vertex operator algebra associated with a rank two root lattice of type A was discovered and its properties were studied. In particular its automorphism group was determined and its simple modules were classified. The results were written in a joint paper Ternary codes and vertex operator algebras. Relations between this vertex operator algebra and the Monster module still remain to be studied. Moreover, Borwein type identity was studied from a point of view of vertex operator algebra. The results were written in a joint paper Borwein identity and vertex opertor algebras.In 1998 all highest weight vectors with weight at most two of a vertex operator algebra associated with a root lattice of type A were classified. Highest weight vectors are important, because once they are known then a vertex operator algebra can be decomposed into a direct sum of simple modules for a tensor product of Virasoro vertex operator algebras. Although not all highest weight vectors are known, much information about the structure of the vertex operator algebra can be obtained from highest weight vectors with weight at most two. For example, a vertex operator algebra having a symmetry of order 4 was constructed by using these highest weight vectors. Recently all highest weight vectors were classified in the case of rank three root lattice of type A.In order to generalize this result to a root lattice of arbitrary rank, a new idea would be required.

在1997年，发现了与A型A型A型两个根晶格相关的顶点操作员代数的三个对称级的子代数，并研究了其性质。特别是确定其自动形态组，并将其简单模块分类。结果写在联合纸三元法规和顶点操作员代数中。该顶点操作员代数与怪物模块之间的关系仍有待研究。此外，从顶点操作员代数的角度研究了Borwein类型的身份。结果写在联合纸borwein身份和顶点opertor代数中。在1998年，所有最高权重向量具有重量，最多是两个顶点操作员代数，与A型的根晶格相关。最高的权重矢量很重要，因为一旦知道了它们，就可以将顶点操作员代数分解为直接的简单模块总和，以构成Virasoro Vertex Operator代数的张量产品。尽管并非所有最高权重向量都是已知的，但有关顶点操作员代数的结构的大量信息最多可以从具有重量的最高权重向量获得。例如，通过使用这些最高权重矢量构建具有订单4的对称性的顶点操作员代数。最近，所有最高权重矢量均在等级的三个类型的根晶格中进行了分类。为了将此结果概括为任意等级的根晶格，需要一个新的想法。

项目成果

Iwasaki, S.: "Infinite families of 2- and 3-designs with parameters nu=p+1, kappa=(p-1)/2^i+1, where p odd prime, 2^eT(p-1), e<greater than or equal>2,1<less than or equal>i<less than or " J.Comb.Designs. 5. 95-110 (1997)

Iwasaki, S.：“无限族 2 和 3 设计，参数为 nu=p 1, kappa=(p-1)/2^i 1，其中 p 为奇素数，2^eT(p-1), e

Iwasaki,S.: "A remark on the action of PGL(2,q) and PSL(2,q) on the projective line" Hokkaido Math.J.26. 203-209 (1997)

Iwasaki,S.：“关于 PGL(2,q) 和 PSL(2,q) 在射影线上的作用的评论”Hokkaido Math.J.26。

Kozono,H: "Exterior problem for the stationary Navier-Stokes equations in the Lorentz space" Mathematishe Annalen. 発表予定.

Kozono，H：“洛伦兹空间中的稳态纳维-斯托克斯方程的外部问题”Mathematishe Annalen。

Iawsaki, S.: "A remark on the action of PGL (2, q) and PSL (2, q) on the projective line" Hikkaido Math.J.26. 203-209 (1997)

Iawsaki, S.：“关于 PGL (2, q) 和 PSL (2, q) 在射影线上的作用的评论” Hikkaido Math.J.26。

Kozono, H.: "The Cauchy problem in the Lorentz space for the Navier-Stokes equation in exterior domains" Proc.Fourth MSJ Int.Research Institute. 243-248 (1997)

Kozono, H.：“外部域中纳维-斯托克斯方程的洛伦兹空间中的柯西问题”Proc.Fourth MSJ Int.Research Institute。