| 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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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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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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Report
(4 results)
Research Products
(16 results)
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[Presentation] Monstrous Lie Algebras2013
Author(s)
Scott Carnahan
Organizer
Conference on Moonshine, Mock modular forms, and String theory
Place of Presentation
Simons Center for Geometry and Physics (アメリカ)
Related Report
Invited
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[Presentation] Monstrous Lie Algebras2013
Author(s)
Scott Carnahan
Organizer
Taitung workshop on group theory, VOA and algebraic combinatorics
Place of Presentation
Taitung University, Taiwan
Related Report
Invited
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