Study of representation theory of semisimple Lie groups via Jacquet modules

• Project/Area Number: 23740004
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: ABE Noriyuki 北海道大学, 創成研究機構, 特任助教 (00553629)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: Jacquet加群 / 半単純Lie群 / 放物型誘導表現 / 既約表現 / 半単純リー群 / ジャッケ加群

Research Abstract

I studied the representation theory of a semisimple Lie group. A semisimple Lie group is a class of a continuous group. One example is a orthogonal group which consists of rotations. I especially studied parabolically induced representations via describing its Jacquet module explicitly. I showed some properties of parabolically induced representations which is important to calculate its Jacquet modules.

Research Products

• [Journal Article] Jacquet functor and De Concini-Procesi compactification (2016)
  • Author(s): Noriyuki Abe, Yoichi Mieda
  • Journal Title: International Mathematics Research Notices Volume: 未定 Pages: 3810-3829
  • DOI: 10.1093/imrn/rnu048
  • Peer Reviewed
• [Journal Article] Loewy series of parabolically induced G_1T-Verma modules (2015)
  • Author(s): Noriyuki Abe, Masaharu Kaneda
  • Journal Title: Journal of the Institute of Mathematics of Jussieu Volume: 13 Issue: 1 Pages: 185-220
  • DOI: 10.1017/s1474748014000012
  • Peer Reviewed
• [Journal Article] On a classification of irreducible admissible modulo p representations of a p-adic split reductive group (2013)
  • Author(s): Noriyuki Abe
  • Journal Title: Compositio Mathematica Volume: Volume 149, Issue 12 Pages: 2139-2168
  • Peer Reviewed
• [Journal Article] The category O for a general Coxeter system (2012)
  • Author(s): Noriyuki Abe
  • Journal Title: J. Algebra Volume: Volume 367, 1 October 2012 Pages: 1-25
  • Peer Reviewed
• [Journal Article] Generalized Jacquet Modules of Parabolically Induced Representations (2012)
  • Author(s): Noriyuki Abe
  • Journal Title: Publ. Res. Inst. Math. Sci. Volume: Volume 48, Issue 2 Pages: 419-473
  • NAID: 110009424737
  • Peer Reviewed
• [Journal Article] The category O for a general Coxeter system (2012)
  • Author(s): N. Abe
  • Journal Title: Journal of Algebra Volume: 367 Pages: 1-25
  • DOI: 10.1016/j.jalgebra.2012.06.002
  • Peer Reviewed
• [Presentation] "Change of weight" theorem (2014)
  • Author(s): 阿部紀行
  • Organizer: Workshop on modular Iwahori-Heckealgebras
  • Place of Presentation: Humboldt University,ドイツ
  • Year and Date: 2014-03-20
• [Presentation] プロ p岩堀 Hecke環の法 p表現について (2014)
  • Author(s): 阿部紀行
  • Organizer: 九州代数的整数論 2014
  • Place of Presentation: 九州大学
  • Year and Date: 2014-02-06
• [Presentation] On a modulo p representation of pro-p Iwahori-Hecke algebra (2014)
  • Author(s): 阿部紀行
  • Organizer: Conference on Local Langlands Conjecture
  • Place of Presentation: Tata Institute of Fundamental Research, インド
  • Year and Date: 2014-01-03
• [Presentation] On a modulo p representation of pro-p Iwahori-Hecke algebra (2014)
  • Author(s): Noriyuki Abe
  • Organizer: Conference on Local Langlands Conjecture
  • Place of Presentation: Tata Institute of Fundamental Research（インド）
  • Invited
• [Presentation] プロp岩堀Hecke環の法p表現について (2014)
  • Author(s): 阿部紀行
  • Organizer: 九州代数的整数論2014
  • Place of Presentation: 九州大学（福岡市）
• [Presentation] "Change of weight" theorem (2014)
  • Author(s): Noriyuki Abe
  • Organizer: Workshop on modular Iwahori-Hecke algebras
  • Place of Presentation: Humboldt University（ドイツ）
  • Invited
• [Presentation] p進簡約群の既約法 p許容表現の分類について (2013)
  • Author(s): 阿部紀行
  • Organizer: 代数的整数論とその周辺
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2013-12-12
• [Presentation] On modulo p representations of pro-p Iwahori-Hecke algebra (2013)
  • Author(s): 阿部紀行
  • Organizer: 2013年度表現論シンポジウム
  • Place of Presentation: 三浦
  • Year and Date: 2013-11-28
• [Presentation] On a Classification of Irreducible Modulo p Representations of p-adic Groups (2013)
  • Author(s): 阿部紀行
  • Organizer: The 2nd Pacific Rim Mathematical Association Congress (special session, Number Theory andRepresentation Theory)
  • Place of Presentation: 上海
  • Year and Date: 2013-06-24
• [Presentation] p進簡約群の法 p表現の分類について (2013)
  • Author(s): 阿部紀行
  • Organizer: 代数セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2013-05-09
• [Presentation] On a modulo p representation of pro-p Iwahori-Hecke algebra (2013)
  • Author(s): 阿部紀行
  • Organizer: Modular Representation Theory of Finite and p-adic Groups
  • Place of Presentation: Institute for Mathematical Sciences, NationalUniversity of Singapore
  • Year and Date: 2013-04-22
• [Presentation] On a classification of irreducible modulo p representations of a split p-adic group (2013)
  • Author(s): 阿部紀行
  • Organizer: Seminaire Groupes Reductifs et FormesAutomorphes
  • Place of Presentation: パリ 6大学, Jussieu
  • Year and Date: 2013-02-18
• [Presentation] A classfication of irreducible admissible modulo p representations of reductive p-adic groups (2013)
  • Author(s): 阿部紀行
  • Organizer: Workshop on Local Langlands Conjecture
  • Place of Presentation: Tata Institute of Fundamental Research,インド
• [Presentation] On a modulo p representation of pro-p Iwahori-Hecke algebra (2013)
  • Author(s): Noriyuki Abe
  • Organizer: Modular Representation Theory of Finite and p-adic Groups
  • Place of Presentation: National University of Singapore（シンガポール）
  • Invited
• [Presentation] p進簡約群の法p表現の分類について (2013)
  • Author(s): 阿部紀行
  • Organizer: 代数セミナー,
  • Place of Presentation: 東北大学（仙台市）
• [Presentation] On a Classification of Irreducible Modulo p Representations of p-adic Groups (2013)
  • Author(s): Noriyuki Abe
  • Organizer: The 2nd Pacific Rim Mathematical Association Congress
  • Place of Presentation: 上海交通大学（中国）
  • Invited
• [Presentation] On modulo p representations of pro-p Iwahori-Hecke algebra (2013)
  • Author(s): 阿部紀行
  • Organizer: 2013年度表現論シンポジウム
  • Place of Presentation: マホロバ・マインズ三浦
• [Presentation] p進簡約群の既約法p許容表現の分類について (2013)
  • Author(s): 阿部紀行
  • Organizer: 代数的整数論とその周辺
  • Place of Presentation: 京都大学数理解析研究所（京都市）
• [Presentation] A classication of irreducible admissible modulo p representations of reductive p-adic groups (2013)
  • Author(s): Noriyuki Abe
  • Organizer: Workshop on Local Langlands Conjecture
  • Place of Presentation: Tata Institute of Fundamental Research（インド）
  • Invited
• [Presentation] q=0のaffineHecke環について (2012)
  • Author(s): 阿部紀行
  • Organizer: 表現論ワークショップ
  • Place of Presentation: 鳥取
  • Year and Date: 2012-12-26
• [Presentation] 制限普遍包絡環の放物型誘導表現の剛性と Loewy series (2012)
  • Author(s): 阿部紀行
  • Organizer: 表現論セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2012-10-31
• [Presentation] 分裂型 p進簡約群の既約認容法p表現の分類について (2012)
  • Author(s): 阿部紀行
  • Organizer: 大阪大学整数論&保型形式セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2012-06-15
• [Presentation] On a structure of modulo p compact induction of split p-adic groups (2012)
  • Author(s): 阿部紀行
  • Organizer: Workshop on the p-adic Langlands program
  • Place of Presentation: Fields institute
  • Year and Date: 2012-04-23
• [Presentation] Geometric realization of Jacquet functor via symmetric space (2012)
  • Author(s): 阿部紀行
  • Organizer: Lie Theory seminar
  • Place of Presentation: 香港科技大学
  • Year and Date: 2012-02-07
• [Presentation] 対称空間のコンパクト化による Jacquet加群の実現 (2011)
  • Author(s): 阿部紀行
  • Organizer: Kyoto Representation Seminar
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-11-11
• [Presentation] 分裂型 p進簡約群の法 p表現の分類について (2011)
  • Author(s): 阿部紀行
  • Organizer: 2011年度表現論シンポジウム
  • Place of Presentation: 南部
  • Year and Date: 2011-11-10
• [Presentation] On a classification of irreducible modulo p representationsof a split p-adic group (2011)
  • Author(s): 阿部紀行
  • Place of Presentation: 数物宇宙連携機構
  • Year and Date: 2011-10-27
• [Presentation] On a classification of irreducible admissible moduleo p representations of a split p-adic group (2011)
  • Author(s): 阿部紀行
  • Organizer: Analysis on Lie Groups
  • Place of Presentation: Max Planck institute for Mathematics
  • Year and Date: 2011-09-21
• [Presentation] Extension between Verma modules and R-polynomial (2011)
  • Author(s): 阿部紀行
  • Organizer: Algebraic Representation Theory Conference
  • Place of Presentation: Upsala University
  • Year and Date: 2011-09-02
• [Presentation] On a classification of irreducible admissible modulo p representations of a split p-adic group (2011)
  • Author(s): 阿部紀行
  • Organizer: Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces
  • Place of Presentation: 京都大学
  • Year and Date: 2011-07-05
• [Presentation] 分裂型 p進簡約群の既約許容法p表現の分類について (2011)
  • Author(s): 阿部紀行
  • Organizer: 大阪表現論セミナー
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2011-06-20
• [Presentation] On a classification of irreducible admissible modulo p representations of a split p-adic group (2011)
  • Author(s): 阿部紀行
  • Organizer: 2011 Nankai International Workshop on Representation Theory and Harmonic Analysis
  • Place of Presentation: 南開大学
  • Year and Date: 2011-06-08
• [Presentation] 対称空間のコンパクト化によるJacquet加群の幾何学的実現について (2011)
  • Author(s): 阿部紀行
  • Organizer: 代数群と量子群の表現論研究集会
  • Place of Presentation: 小豆島
  • Year and Date: 2011-06-03
• [Presentation] 分裂型 p進簡約群の既約許容法p表現の分類について (2011)
  • Author(s): 阿部紀行
  • Organizer: 代数学セミナー
  • Place of Presentation: 九州大学
  • Year and Date: 2011-05-20
• [Presentation] 分裂型 p進簡約群の既約許容法p表現の分類について (2011)
  • Author(s): 阿部紀行
  • Organizer: 談話会
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-05-12
• [Presentation] 対称空間のコンパクト化によるJacquet加群の幾何学的実現について (2011)
  • Author(s): 阿部紀行
  • Organizer: 表現論セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-04-25
• [Presentation] 対称空間のコンパクト化によるJacquet 加群の幾何学的実現について (2011)
  • Author(s): 阿部 紀行
  • Organizer: 代数群と量子群の表現論研究集会(招待講演)
  • Place of Presentation: 国民宿舎 小豆島（香川県）
• [Presentation] On a classification of irreducible admissible modulo p representations of a split p-adic group (2011)
  • Author(s): Noriyuki Abe
  • Organizer: 2011 Nankai International Workshop on Representation Theory and Harmonic Analysis(招待講演)
  • Place of Presentation: 南開大学（中国）
• [Presentation] Extension between Verma modules and R-polynomial (2011)
  • Author(s): Noriyuki Abe
  • Organizer: Algebraic Representation Theory Conference(招待講演)
  • Place of Presentation: Upsala University（スウェーデン）
• [Presentation] 分裂型p進簡約群の法p表現の分類について (2011)
  • Author(s): 阿部 紀行
  • Organizer: 表現論シンポジウム
  • Place of Presentation: 国民宿舎 紀州路みなべ（和歌山県）