Research on automorphic representation

• Project/Area Number: 21340007
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: IKEDA Tamotsu 京都大学, 理学(系)研究科(研究院), 教授 (20211716)
• Co-Investigator(Renkei-kenkyūsha): YOSHIDA Hiroyuki 京都大学, 大学院理学研究科, 名誉教授 (40108973) ; ICHINO Atsushi 京都大学, 大学院理学研究科, 准教授 (40347480) ; HIRAGA Kaoru 京都大学, 大学院理学研究科, 講師 (10260605)
• Project Period (FY): 2009-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥12,610,000 (Direct Cost: ¥9,700,000、Indirect Cost: ¥2,910,000); Fiscal Year 2013: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2010: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2009: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
• Keywords: 保型形式 / 保型表現 / 保型的L関数 / 保型形式の周期 / ヒルベルト保型形式 / ジーゲル保型形式 / 調和解析

Outline of Final Research Achievements

A. Ichino and T. Ikeda published a paper on periods of Gross-Prasad type. K. Hiraga wrote a paper on the trace formula on inner forms of special linear group with H. Saito. H.Yoshida publiched a paper on motivic Galois groups and L-groups.
A. Ichino wrote a paper on period of Gross-Prasad type on special orthogonal group of size 4 and 5 with W. Gan. This is an interesting example of the period relation. K. Hiraga and T. Ikeda constructed a Kohnen plus space for Hilbert modular forms of half-integral weight.

Research Products

• [Journal Article] On the Kohnen plus space for Hilbert modular forms of half-integral weight I (2013)
  • Author(s): Kaoru Hiraga and Tamotsu Ikeda
  • Journal Title: Compositio Math. Volume: 149 Issue: 12 Pages: 1963-2010
  • DOI: 10.1112/s0010437x13007276
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the periods of automorphic forms on special orthogonal groups and the Gross -Prasad conjecture (2010)
  • Author(s): A.Ichino, T.Ikeda
  • Journal Title: Geom.Funct.Anal. 19 Pages: 1378-1425
  • Peer Reviewed
• [Journal Article] Motivic Galois groups and L-groups
  • Author(s): Yoshida, Hiroyuki
  • Journal Title: Clay Mathematics Proceedings (掲載確定)
  • Peer Reviewed
• [Presentation] Hilbert modular form に関する Kohnen plus space について (2013)
  • Author(s): 池田保
  • Organizer: Colloquium
  • Place of Presentation: 九州大学数理学研究院
  • Year and Date: 2013-11-28
  • Invited
• [Presentation] On the stabilization of the trace formula of the covering group of SL_2 (2013)
  • Author(s): Tamotsu Ikeda
  • Organizer: Automorphic forms and harmonic analysis on covering groups
  • Place of Presentation: American Institute of Mathmetics
  • Year and Date: 2013-06-13
  • Invited
• [Presentation] On Kohnen plus space for Hilbert modular forms of half-integral weight (2011)
  • Author(s): T.Ikeda
  • Organizer: Explicit theory of automorphic forms, applications and computations
  • Place of Presentation: CIRM, Luminy(フランス)(招待講演)
  • Year and Date: 2011-05-10
• [Presentation] On Kohnen plus space for Hilbert modular forms of half-integral weight (2011)
  • Author(s): T.Ikeda
  • Organizer: Ueda Memorial Conference on Automorphic Forms
  • Place of Presentation: 奈良女子大学(奈良県)(招待講演)
  • Year and Date: 2011-01-26
• [Presentation] SL_2の被覆群の跡公式とその応用 (2011)
  • Author(s): 池田保
  • Organizer: 保型形式と関連する跡公式,ゼータ関数の研究
  • Place of Presentation: 数理解析研究所(京都府)(招待講演)
  • Year and Date: 2011-01-19
• [Presentation] Formal degrees and adjoint gamma factors (2010)
  • Author(s): A.Ichino
  • Organizer: Group Theory/Lie Theory/Number Theory Seminar
  • Place of Presentation: University of Michigan (アメリカ合衆国)
  • Year and Date: 2010-03-22
• [Presentation] On the Kottwitz-Shelstad normalization of the transfer factor for automorphic induction of GL(n) (2010)
  • Author(s): A.Ichino
  • Organizer: 保型形式・保型表現およびそれに伴うL函数と周期の研究
  • Place of Presentation: 東京大学 (東京都)
  • Year and Date: 2010-01-20
• [Presentation] ユニタリ群の安定跡公式 (2010)
  • Author(s): 平賀郁
  • Organizer: 整数論サマースクール「アーサー・セルバーグ跡公式入門」
  • Place of Presentation: 河鹿荘ロイヤルホテル(石川県)(招待講演)
• [Presentation] Formal degrees and local theta correspondence (2009)
  • Author(s): A.Ichino
  • Organizer: 金沢数論幾何集会
  • Place of Presentation: 金沢大学 (石川県)
  • Year and Date: 2009-11-25
• [Presentation] Theta functions from the representation -theoretic viewpoint (2009)
  • Author(s): A.Ichino
  • Organizer: Pohang Mathematics Institute 2009
  • Place of Presentation: POSTECH (韓国)
  • Year and Date: 2009-11-21
• [Presentation] 保型形式の周期とL関数の特殊値 (2009)
  • Author(s): A.Ichino
  • Organizer: 九州大学 談話会
  • Place of Presentation: 九州大学 (福岡県)
  • Year and Date: 2009-10-21
• [Presentation] 表現論と数論的不変量 (2009)
  • Author(s): A.Ichino
  • Organizer: 大阪市立大学 談話会
  • Place of Presentation: 大阪市立大学 (大阪府)
  • Year and Date: 2009-10-06
• [Presentation] SL (N) の L-indistinguishability : 局所ラングランズ対応とエンドスコピー (2009)
  • Author(s): 平賀郁
  • Organizer: 日本数学会特別講演
  • Place of Presentation: 大阪大学 (大阪府)
  • Year and Date: 2009-09-24
• [Presentation] On endoscopy and the refined Gross-Prasad conjecture for (S05, S04) (2009)
  • Author(s): A.Ichino
  • Organizer: 第12回整数論オータムワークショップ白馬
  • Place of Presentation: 白馬ハイパウントホテル (長野県)
  • Year and Date: 2009-09-11
• [Presentation] lifting of hermitian modular forms in the case the class number is greater than one (2009)
  • Author(s): T.Ikeda
  • Organizer: 第12回整数論オータムワークショップ白馬
  • Place of Presentation: 白馬ハイマウントホテル (長野県)
  • Year and Date: 2009-09-10
• [Presentation] 明示的周期公式の定式化 (一般化の試み) (2009)
  • Author(s): T.Ikeda
  • Organizer: 第12回整数論オータムワークショップ白馬
  • Place of Presentation: 白馬ハイマウントホテル (長野県)
  • Year and Date: 2009-09-08
• [Presentation] 明示的周期公式の定式化 (Gross-Prasad case) (2009)
  • Author(s): A.Ichino
  • Organizer: 第12回整数論オータムワークショップ白馬
  • Place of Presentation: 白馬ハイパウントホテル (長野県)
  • Year and Date: 2009-09-08
• [Presentation] Cohomology and L-values (2009)
  • Author(s): Hiroyuki Yoshida
  • Organizer: Zeta function days in Seoul
  • Place of Presentation: 延世 (Yonsei) 大学 (韓国)
  • Year and Date: 2009-09-04
• [Presentation] Relative trace formula and periods of automorphic forms (2009)
  • Author(s): A.Ichino
  • Organizer: American Institute of Mathematics
  • Place of Presentation: AIM (アメリカ合衆国)
  • Year and Date: 2009-08-25
• [Presentation] CM-periods (2009)
  • Author(s): Hiroyuki Yoshida
  • Organizer: Workshop on higher rank L-functions and computations
  • Place of Presentation: Centro Ciencias de Benasque Pedro Pascual (Spain)
  • Year and Date: 2009-07-31
• [Presentation] Formal degrees and adjoint gamma factors (2009)
  • Author(s): A.Ichino
  • Organizer: Workshop on Geometry Related to the Langlands Programme
  • Place of Presentation: University of Ottawa (アメリカ合衆国)
  • Year and Date: 2009-05-30
• [Presentation] Duke-Imamoglu lifting for Hilbert-Siegel modular forms
  • Author(s): T. Ikeda
  • Organizer: Pan Asian Number Theory conference 2012
  • Place of Presentation: Indian Institute of Science Education and Research (IISER), Pune, India
  • Invited
• [Presentation] Kohnen plus spaces for Hilbert modular forms of half-integral weight (joint work with K. Hiraga)
  • Author(s): T. Ikeda
  • Organizer: Japan-Taiwan Number Theory Conference
  • Place of Presentation: National center of theoretical science, Taiwan
  • Invited
• [Presentation] Lifting and thier periods
  • Author(s): T. Ikeda
  • Organizer: The 15th Autumn Workshop on Number Theory
  • Place of Presentation: 白馬ハイマウントホテル（長野県白馬村）
  • Invited
• [Presentation] Stabilization of the trace formula for the covering group of SL_2 and its application to the theory of Kohnen plus spaces (joint work with K. Hiraga)
  • Author(s): T. Ikeda
  • Organizer: Pan Asian Number Theory Conference in Beijing
  • Place of Presentation: Morningside Center of Mathematics, Beijing, China
  • Invited
• [Presentation] Hilbert modular form に関する Kohnen plus space について
  • Author(s): 池田保
  • Organizer: 九州大学代数学セミナー
  • Place of Presentation: 九州大学
  • Invited
• [Presentation] Stabilization of the trace formula for the covering group of SL_2 and its application to the theory of Kohnen plus spaces (joint work with K. Hiraga)
  • Author(s): T. Ikeda
  • Organizer: Blanching Laws
  • Place of Presentation: National University of Singapore, Singapore
  • Invited