2019 Fiscal Year Final Research Report
Beyond Generalized Moonshine
| Project/Area Number |
17K14152
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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) |
2017-04-01 – 2020-03-31
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| Keywords | 代数 / ムーンシャイン / 頂点作用素代数 / モジュラー形式 |
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| Outline of Final Research Achievements |
In this project, I have four main results:1) I have constructed a self-dual integral form of the Moonshine vertex operator algebra, with monster symmetry. This resolves Ryba's 1994 Modular moonshine conjecture. 2) I strengthened my earlier proof of the Generalized Moonshine conjecture, by showing that a collection of ambiguous constants are roots of unity. 3) I proved Tuite's 1993 orbifold duality conjecture, connecting non-Fricke elements of the monster to certain fixed-point free automorphisms of the Leech lattice. 4) Together with T. Komuro and S. Urano, I showed that 154 of the 157 non-monstrous completely replicable functions cannot arise as traces of automorphisms of holomorphic vertex operator algebras.
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| Free Research Field |
数学
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| Academic Significance and Societal Importance of the Research Achievements |
Monstrous moonshine is a mathematical phenomenon that was discovered when someone noticed some large numbers from calculations in two different fields of mathematics were very similar. My work in this project has answered some old questions about the nature of this connection and similar phenomena.
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