Study of representation theory of semisimple Lie groups via investigating parabolic inductions

• Project/Area Number: 21840016
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: ABE Noriyuki The University of Tokyo, 大学院・数理科学研究科, 特任助教 (00553629)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,496,000 (Direct Cost: ¥1,920,000、Indirect Cost: ¥576,000); Fiscal Year 2010: ¥1,209,000 (Direct Cost: ¥930,000、Indirect Cost: ¥279,000); Fiscal Year 2009: ¥1,287,000 (Direct Cost: ¥990,000、Indirect Cost: ¥297,000)
• Keywords: 半単純Lie群 / 放物型誘導表現 / Jacquet加群

Research Abstract

The aim of this study is to investigate the structure of parabolic induction of a semisimple Lie group via calculating its Jacquet module. I noticed that more direct description than I expected can be obtained. New frameworks are needed for such a description. Some of them are established.

Research Products

• [Journal Article] On the existence of homomorphisms between principal series representations of complex semisimple Lie groups (2011)
  • Author(s): Noriyuki Abe
  • Journal Title: J.Algebra 330,no.1 Pages: 468-481
  • Peer Reviewed
• [Journal Article] On the existence of homomorphisms between principal series representations of complex semisimple Lie groups (2011)
  • Author(s): Noriyuki Abe
  • Journal Title: Journal of Algebra Volume: 330 Pages: 468-481
  • Peer Reviewed
• [Journal Article] A remark on the geometric Jacquet functor (2010)
  • Author(s): Noriyuki Abe, Yoichi Mieda
  • Journal Title: J.Math.Sci.Tokyo 17 Pages: 243-246
  • NAID: 120006906055
  • Peer Reviewed
• [Journal Article] A remark on the geometric Jacquet functor (2010)
  • Author(s): Noriyuki Abe, Yoichi Mieda
  • Journal Title: Journal of Mathematical Sciences, The University of Tokyo Volume: 17 Pages: 243-246
  • NAID: 120006906055
  • Peer Reviewed
• [Journal Article] General heart construction on a triangulated category (II) : Associated cohomological functor
  • Author(s): Noriyuki Abe, Hiroyuki Nakaoka
  • Journal Title: Applied Categorical Structures
  • Peer Reviewed
• [Journal Article] General heart construction on a triangulated category (II) : Associated cohomological functor
  • Author(s): Noriyuki Abe, Hiroyuki Nakaoka
  • Journal Title: Applied Categorical Structures (掲載確定)
  • Peer Reviewed
• [Presentation] Verma加群の拡大とR多項式 (2010)
  • Organizer: 2010年度表現論シンポジウム
  • Place of Presentation: 伊豆の国市
  • Year and Date: 2010-11-12
• [Presentation] 複素半単純Lie群の主系列表現の間のExt群について (2010)
  • Organizer: 日本数学会秋季総合分科会特別講演
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] 複素半単純Lie群の主系列表現の間のExt群について (2010)
  • Author(s): 阿部紀行
  • Organizer: 日本数学会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] Jacquet modules of parabolically induced representation (2010)
  • Organizer: 2010 Nankai Summer School on Representation Theory and Harmonic Analysis
  • Place of Presentation: 南開大学
  • Year and Date: 2010-06-11
• [Presentation] On the extensions between Verma modules (2010)
  • Organizer: Recent Advances in Mathematics at IPMU
  • Place of Presentation: 2,IPMU
  • Year and Date: 2010-04-06
• [Presentation] On extensions between principal series of complex semisimple Lie groups (2010)
  • Organizer: 第9回冪零軌道と表現論研究集会
  • Place of Presentation: 北海道大学
  • Year and Date: 2010-02-19
• [Presentation] On the existence of homomorphisms between principal series of complex semisimple Lie groups (2009)
  • Organizer: Tokyo-Seoul Conference in Mathematics Representation Theory
  • Place of Presentation: 東京大学
  • Year and Date: 2009-12-04
• [Presentation] On dimension of Whittaker vectors (2009)
  • Organizer: 金沢数論幾何集会
  • Place of Presentation: 金沢
  • Year and Date: 2009-11-26
• [Presentation] Jacquet modules of parabolic induction (2009)
  • Organizer: AGU Lectures on Representation Theory
  • Place of Presentation: 青山学院大学
  • Year and Date: 2009-10-22
• [Presentation] ねじれたVerma加群の間の高次Ext群の消滅について (2009)
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] Jacquet modules of parabolic induction (2009)
  • Organizer: Workshop on Integral Geometry and Group Representations
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2009-08-10
• [Presentation] The category O for a general Coxeter system (2009)
  • Organizer: RIMS研究集会「群の表現と非可換調和解析の新展開」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-06-03