2019 Fiscal Year Final Research Report
Noncommutative Deligne-Lusztig theory
| Project/Area Number |
17K18722
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| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra, Geometry, and related fields
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Imai Naoki 東京大学, 大学院数理科学研究科, 准教授 (90597775)
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| Project Period (FY) |
2017-06-30 – 2020-03-31
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| Keywords | Deligne-Lusztig 構成 |
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| Outline of Final Research Achievements |
By considering an analogue of Deligne-Lusztig theory, we constructed representations which we are interested in from a number theoretic view point. More concretely, we constructed a Weil representation for a finite unitary group and its Shintani lift geometrically. Further, using an Frobenius action, we constructed and studied the Howe correspondence for a symplectic group in a special case. We studied also mod ell Weil representations and mod ell Howe correspondences.
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| Free Research Field |
数論
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| Academic Significance and Societal Importance of the Research Achievements |
数論的に興味深い表現を幾何学的に構成することができた．またその構成を用いて，新谷リフトのような関手性を幾何学的に実現したり，表現に関する性質を幾何的な手法を用いて調べることができた．さらに幾何学的に実現できていることを用いて mod ell 係数における類似の対象を自然に構成し，それらについても幾何的に調べて新しい結果が得られた．modular 表現は数論においても重要な役割を果たすため，今後の応用も期待でき，学術的意義があると考えられる．
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