Modular invariance of vertex operator algebras and its application to representation theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800003
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: University of Tsukuba
• Principal Investigator: ARIKE Yusuke 筑波大学, 数理物質系, 助教 (50583770)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 頂点作用素代数 / モジュラー不変性 / モジュラー微分方程式 / ヴィラソロ代数 / 大域次元

Outline of Final Research Achievements

We study several relations between characters of simple modules of vertex operator algebras and modular linear differential equations and obtain the following results. (i) We prove that if the dimension of characters of simple affine vertex operator algebras is less than 6 and greater than 1, then the space of characters is a solution space of a modular linear differential equation. (ii) We give a characterization of Virasoro vertex operator algebras by means of modular linear differential equations. (iii) We show that there are no good vertex operator algebras with central charges 164/5 and 236/7 whose characters are solutions of modular linear differential equations of order 3.

Free Research Field

頂点作用素代数