Studies on vertex operator algebras and various phenomena similar to moonshine

2015 Fiscal Year Final Research Report

• Project/Area Number: 26610004
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: MATSUO Atsushi 東京大学, 数理(科)学研究科(研究院), 准教授 (20238968)
• Co-Investigator(Renkei-kenkyūsha): YAMAUCHI Hiroshi 東京女子大学, 現代教養学部, 准教授 (40452213)
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: 頂点作用素代数 / 単純リー環 / 極小巾零軌道

Outline of Final Research Achievements

In order to understand various phenomena similar to moonshine in a uniform manner, we have considered several problems related to them. Among others, in a joint work with Maruoka and Shimakura on vertex operator algebras having large symmetries, we have classified those with minimal conformal weight one, and obtained that the simple Lie algebras belonging to Deligne exceptional series arise. We have also considered the Hilbert series of minimal nilpotent orbits of simple Lie algebrasin a joint work with A.P. Veselov and obtained a universal formula expressing the Hilbert series and the degree of the adjoint variety.

Free Research Field

無限次元リー環の表現論