2014 Fiscal Year Final Research Report
Project/Area Number 
24740005

Research Category 
GrantinAid for Young Scientists (B)

Allocation Type  Multiyear Fund 
Research Field 
Algebra

Research Institution  University of Tsukuba 
Principal Investigator 

Project Period (FY) 
20120401 – 20150331

Keywords  代数 / ムーンシャイン 
Outline of Final Research Achievements 
I have developed the theory of conformal blocks on twisted nodal algebraic curves using logarithmic geometry, and applied this to the discovery of fusion rules and higher associativity data for twisted modules of the monster vertex algebra. For this purpose, I have also introduced general theories of higher frames for smooth morphisms, and infinite dimensional crystalline descent theorems. I gave a method for constructing vertex algebras and abelian intertwining algebras, given a family of modules, intertwining operators, and higher associativity data. I applied this construction to twisted modules of the monster vertex algebra, and produced a family of infinite dimensional Lie algebras with actions of large finite groups. By the results of this research, I have proved many cases of the generalized moonshine conjecture, in particular for the classes pA in the monster for all primes p.

Free Research Field 
数学
