2014 Fiscal Year Final Research Report
| Project/Area Number |
24740005
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
|
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 代数 / ムーンシャイン |
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| 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.
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| Free Research Field |
数学
|
