2010 Fiscal Year Final Research Report
Research on irreducible representations of W-algebras by using lattice vertex operator algebras
| Project/Area Number |
20540012
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Hitotsubashi University |
|---|
Principal Investigator |
YAMADA Hiromichi Hitotsubashi University, 大学院・経済学研究科, 教授 (50134888)
|
|---|
| Research Collaborator |
ARAKAWA Tomoyuki 京都大学, 数理解析研究所, 准教授 (40377974)
TANABE Kenichiro 北海道大学, 大学院・理学研究院, 准教授 (10334038)
DONG Chongying University of California, Department of Mathematics(アメリカ), 教授
LAM Ching Hung Academia Sinica(台湾), 教授
WANG Qing Xiamen University, School of Mathematics(中国), 助教授
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Keywords | 頂点作用素代数 / W代数 |
|---|
| Research Abstract |
We study parafermion vertex operator algebras, which form an important family of W-algebras. Its irreducible modules are constructed by using the theory of lattice vertex operator algebras. The operator product expansions among the four generators are obtained. Moreover, the singular vectors of weight 8, 9, and 10 are determined. In the case of small level k, we calculate another singular vector of weight k+1. We use the singular vector to classify the irreducible modules and establish rationality and C2-cofiniteness.
|
