| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We had worked on the classification problem of vertex operator algebras (simply VOAs). The sets of characters were expected to characterize VOAs. However, there are examples of VOAs whose have the same set of characters but they are not isomorphic. Therefore we intended the classification by using modular linear differential equations (MLDEs for short) since any set of characters of a VOA is a subspace of the space of solutions of an MLDE. We achieved the classification of the Virasoro VOA (the so-called the minimal model) under very mild conditions. Moreover, since it is very important to have a recipe to obtain MLDEs of higher order. We found that the Rankin-Cohen brackets give a general description of MLDEs. This result contributes to the theory of modular forms by giving a new differential operator which generalizes the Serre operation.
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