Arithmetic structure of automorphic representations and endoscopy
| Project/Area Number |
25400015
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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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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
KONNO Takuya 九州大学, 数理(科)学研究科(研究院), 准教授 (00274431)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 保型形式 / テータ対応 / L関数 / 周期 / 保型内視論 / テータリフト |
|---|
| Outline of Final Research Achievements |
Periods and Fourier coefficients of automorphic forms are generalized to automorphic representations. We hope to extend the various arithmetic properties of former objects to automorphic representations. For this we need to describe local properties of automorphic representations. Recently, the automorphic representations of classical groups are classified in terms of the theory of (twisted) endoscopy. We revise the local theory of this classification for low rank groups using specific normalizations which are useful for the study of periods. Further, to analyze automorphic representations of non-quasisplit groups, we prove the Iwasawa decomposition for general reductive adele groups using the Bruhat-Tits theory.
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Report
(4 results)
Research Products
(5 results)
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[Presentation] 高さ関数とその性質2014
Author(s)
今野拓也
Organizer
福岡保型形式ミニ研究集会
Place of Presentation
九州大学理学部(箱崎キャンパス)
Year and Date
2014-06-20 – 2014-06-22
Related Report
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[Presentation] アデール群の構造22014
Author(s)
今野拓也
Organizer
熊本保型形式ミニ研究集会
Place of Presentation
熊本大学
Year and Date
2014-05-16 – 2014-05-18
Related Report
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