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On L-packets of reductive algebraic groups

Research Project

Project/Area Number 18340006
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKyoto University

Principal Investigator

SAITO Hiroshi  京大, 理学(系)研究科(研究院), 教授 (20025464)

Co-Investigator(Kenkyū-buntansha) 西山 享  京都大学, 大学院・理学研究科, 准教授 (70183085)
池田 保  京都大学, 大学院・理学研究科, 教授 (20211716)
平賀 郁  京都大学, 大学院・理学研究科, 講師 (10260605)
古澤 昌秋  大阪市立大学, 大学院・理学研究科, 教授 (50294525)
市野 篤史  大阪市立大学, 大学院・理学研究科, 准教授 (40347480)
高橋 哲也  大阪府立大学, 総合教育研究機構, 教授 (20212011)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥10,330,000 (Direct Cost: ¥8,500,000、Indirect Cost: ¥1,830,000)
Fiscal Year 2009: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2008: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2007: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2006: ¥2,400,000 (Direct Cost: ¥2,400,000)
Keywords数論 / 保型表現 / エルパケット / アーサーパケット / 許容表現 / 表現の制限則 / テータ対応 / グロスプラサド予想 / 跡公式 / S群 / 表現の制限 / エンドスコピー / 特殊ユニタリ群 / 形式的次数 / エルパラメータ / エス群 / シーソー原理
Research Abstract

(1) エンドスコピ-、エルパラメ-タ-の理論は、簡約代数群の表現の理論において、重要な役割を果たすと思われるが、この研究の第一の目標は、エンドスコピ-、エルパラメ-タの理論と、局所体、大局体上の簡約代数群の保型表現の関係を探ることである。
(2) もう一つの目標は、簡約代数群のエルパケット、ア-サ-パケットの決定、特に表現の制限即の記述による、特殊線形群、特殊ユニタリ群の inner form のエルパケット、ア-サ-パケットの決定である。

Report

(4 results)
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (15 results)

All 2008 2007 2006

All Journal Article (12 results) (of which Peer Reviewed: 10 results) Presentation (3 results)

  • [Journal Article] On the lifting of hermitian modular forms2008

    • Author(s)
      池田保
    • Journal Title

      Compositio Math 114

      Pages: 1107-1154

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On Maass lifts and the central critical values of triple product of Lfunctions2008

    • Author(s)
      池田保、市野篤史
    • Journal Title

      Amer. J. Math 130

      Pages: 75-114

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Two remarks on a theore of Prasad2008

    • Author(s)
      齋藤裕
    • Journal Title

      Pacific Journal of Math 234

      Pages: 185-199

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Formal degrees and adjoint gamma-factors2008

    • Author(s)
      平賀郁、池田保、市野篤史
    • Journal Title

      Journal of Amer. Math. Soc 21

      Pages: 283-304

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Trilinear forms and the central valuss of triple Product L-funtions2008

    • Author(s)
      市野篤史
    • Journal Title

      Duke math. J. 145

      Pages: 281-307

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the lifting of hermitian modular forms2008

    • Author(s)
      池田保
    • Journal Title

      Cmoition Math. 14

      Pages: 1107-1154

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Intersection of harmonics and Capeli identities for Symmetrie pairs2008

    • Author(s)
      西山享, 和知輝仁, Soq Teck Lee
    • Journal Title

      J. Marh. Soc. Japan 60

      Pages: 955-982

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Formal degrees and adjoint gamma factors2008

    • Author(s)
      池田保、平賀郁、市野篤史
    • Journal Title

      J. Amer. Math. Soc. 21

      Pages: 1283-1304

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On maass lifts and the central values of triple L-functions2008

    • Author(s)
      池田保、市野篤史
    • Journal Title

      Amer. J. Math. 130

      Pages: 75-114

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Two remarks on a theorem of Dipendra Prasad2008

    • Author(s)
      齋藤 裕
    • Journal Title

      Pacific J. math. 236

      Pages: 111-115

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pullback of the lifting of elliptic cusp forms and Miyawaki's conjecture2006

    • Author(s)
      池田 保
    • Journal Title

      Duke Math. J. 131-3

      Pages: 469-497

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Theta lifting of nilpotent orbits for symmetric pairs2006

    • Author(s)
      西山 享, 落合啓之
    • Journal Title

      Trans. Amer. Math. Soc. 358-6

      Pages: 2713-2734

    • Related Report
      2006 Annual Research Report
  • [Presentation] Local Gross-Prasad conjecture for U(2)2008

    • Author(s)
      今野拓也
    • Organizer
      International Symposium on Automorphic Forms, L-functions, and Shimura varieties
    • Place of Presentation
      Inha University
    • Year and Date
      2008-11-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the packets for inner forms of SL(N)2007

    • Author(s)
      平賀郁
    • Organizer
      Japan-France conference on automorphic endoscopy
    • Place of Presentation
      CIRM, Luminy, France
    • Year and Date
      2007-06-12
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] On L-packetss of liner forms of SL(N)2007

    • Author(s)
      平賀郁
    • Organizer
      日仏研究集会Automorphic Endoscopy
    • Place of Presentation
      ルミニー数学研究書
    • Year and Date
      2007-06-12
    • Related Report
      2007 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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