Arithmetic structure of automorphic representations and endoscopy

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400015
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyushu University
• Principal Investigator: KONNO Takuya 九州大学, 数理(科)学研究科(研究院), 准教授 (00274431)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 保型形式 / テータ対応 / L関数 / 周期 / 保型内視論

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.

Free Research Field

代数学