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Studies on the standard Whittaker modules

Research Project

Project/Area Number 24540027
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionAoyama Gakuin University

Principal Investigator

Taniguchi Kenji  青山学院大学, 理工学部, 教授 (20306492)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords標準 Whittaker (g,K)-加群 / リー群の表現論 / 主系列表現 / 標準Whittaker 加群 / Lie群の表現論 / 主系列表現の組成列
Outline of Final Research Achievements

The main topic of this research is the analysis of the structure of the standard Whittaker (g,K)-modules of real reductive Lie groups. Obtained are the following results:
(1) In the cases of Spin(n,1), SL(3,R) and Sp(2,R), we determined the structure of the standard Whittaker (g,K)-modules. As byproducts of this research, we obtained a new method of constructing the central elements of the universal enveloping algebra of orthogonal Lie algebras, and we determined the composition series of the principal series representations of SL(3,R) and Sp(2,R).
(2) We proved that, if the group in question satisfies some conditions, the standard Whittaker (g,K)-modules of this group lie in a part of a coherent family.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (13 results)

All 2016 2015 2014 2013 Other

All Journal Article (6 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 1 results,  Open Access: 1 results) Presentation (5 results) (of which Invited: 1 results) Remarks (2 results)

  • [Journal Article] Socle filtrations of the standard Whittaker (g,K)-modules of Spin(r,1)2015

    • Author(s)
      Kenji Taniguchi
    • Journal Title

      Kyoto J. Math.

      Volume: 55 Issue: 1 Pages: 43-61

    • DOI

      10.1215/21562261-2848115

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Discrete Series Whittaker Functions on Spin(2n,2)2014

    • Author(s)
      Kenji Taniguchi
    • Journal Title

      Journal of Mathematical Sciences, the University of Tokyo

      Volume: 21 Pages: 1-59

    • NAID

      120005678247

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Sp(2,R) の主系列表現の組成列について2014

    • Author(s)
      谷口 健二
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1877 Pages: 104-120

    • Related Report
      2013 Research-status Report
  • [Journal Article] CLOSED ORBITS ON PARTIAL FLAG VARIETIES AND DOUBLE FLAG VARIETY OF FINITE TYPE2014

    • Author(s)
      Kensuke Kondo, Kyo Nishiyama, Hiroyuki Ochiai, Kenji Taniguchi
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 68 Issue: 1 Pages: 113-119

    • DOI

      10.2206/kyushujm.68.113

    • NAID

      130004941519

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the composition series of the standard Whittaker (g,K)-modules2013

    • Author(s)
      Kenji Taniguchi
    • Journal Title

      Transactions of American Mathematical Society

      Volume: 365 Issue: 7 Pages: 3899-3922

    • DOI

      10.1090/s0002-9947-2012-05801-6

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A construction of generators of Z(so_n)2013

    • Author(s)
      Kenji Taniguchi
    • Journal Title

      Josai Mathematical Monographs

      Volume: 6 Pages: 93-108

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 緩増加な Whittaker 関数の特定について2016

    • Author(s)
      谷口健二
    • Organizer
      2015年度表現論ワークショップ
    • Place of Presentation
      鳥取県立生涯学習センター
    • Year and Date
      2016-01-10
    • Related Report
      2015 Annual Research Report
  • [Presentation] 標準 Whittaker (g,K)-加群の組成列2015

    • Author(s)
      谷口 健二
    • Organizer
      日本数学会2015年度年会函数解析分科会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-23
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 標準 Whittaker (g,K)-加群のいくつかの性質について2014

    • Author(s)
      谷口 健二
    • Organizer
      2014年度表現論ワークショップ
    • Place of Presentation
      鳥取県立生涯学習センター
    • Year and Date
      2014-12-27
    • Related Report
      2014 Research-status Report
  • [Presentation] Sp(2,R) の主系列表現の組成列について

    • Author(s)
      谷口 健二
    • Organizer
      RIMS研究集会「表現論および表現論の関連する諸分野の発展」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] Sp(2,R) の主系列表現の組成列について

    • Author(s)
      谷口健二
    • Organizer
      2012年度表現論ワークショップ
    • Place of Presentation
      鳥取県立生涯学習センター
    • Related Report
      2012 Research-status Report
  • [Remarks] 谷口健二のホームページ

    • URL

      http://www.gem.aoyama.ac.jp/~taniken/index-j.html

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
  • [Remarks] 谷口健二のホームページ

    • URL

      http://www.gem.aoyama.ac.jp/~taniken/index-j.html

    • Related Report
      2013 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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