2023 Fiscal Year Final Research Report
Generalizations of modules over vertex algebras and their tensor products
| Project/Area Number |
21K03172
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Tokyo City University (2022-2023)
Hokkaido University (2021) |
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Principal Investigator |
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Keywords | 頂点代数 / 加群 / 自己同型群 / テンソル積 |
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| Outline of Final Research Achievements |
Let V be a vertex algebra of countable dimension and G a finite automorphism group of V. We consider a G-stable finite set S consisting of irreducibly twisted V-modules, and take a direct sum M of all irreducibly modules in S.
The semisimple associative algebra A defined by G and S and the fixed point subalgebra V^G act naturally on M, and we show a Schur-Weyl type duality for their actions. As an application, we show that any irreducible twisted V-module is a completely reducible V^G-module.
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| Free Research Field |
頂点代数
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| Academic Significance and Societal Importance of the Research Achievements |
Vを頂点代数，GをVの自己同型群としたとき，Gによって固定されるVの元の全体V^GはVの部分代数となる．固定部分代数V^G加群は，よい性質をもつ頂点代数の構成への応用があるため，この分野の重要な研究対象となっている．既約V^G加群は，既約ツイステッドV加群の部分加群として全て得ることが出来ると予想されている．この問題に関連して，任意の既約ツイステッドV加群は完全可約V^G加群であることを示した．
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