Study of group representation and differential equations associated with root systems and its applications

• Project/Area Number: 20244008
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: The University of Tokyo
• Principal Investigator: OSHIMA Toshio 東京大学, 大学院・数理科学研究科, 教授 (50011721)
• Co-Investigator(Kenkyū-buntansha): KOBAYASHI Toshiyuki 東京大学, 大学院・数理科学研究科, 教授 (80201490)
• Co-Investigator(Renkei-kenkyūsha): ODA Takayuki 東京大学, 大学院・数理科学研究科, 教授 (10109415) ; MATUMOTO Hisayosi 東京大学, 大学院・数理科学研究科, 准教授 (50272597) ; TERADA Itaru 東京大学, 大学院・数理科学研究科, 准教授 (70180081) ; SEKIGUCHI Hideko 東京大学, 大学院・数理科学研究科, 准教授 (50281134) ; SEKIGUCHI Jiro 東京農工大学, 大学院・共生科学技術研究, 教授 (30117717) ; OCHIAI Hiroyuki 九州大学, マスフォアインダストリ研究所, 教授 (90214163) ; SHIMENO Nobukazu 関西学院大学, 理工学部, 教授 (60254140)
• Project Period (FY): 2008 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥40,300,000 (Direct Cost: ¥31,000,000、Indirect Cost: ¥9,300,000); Fiscal Year 2012: ¥7,800,000 (Direct Cost: ¥6,000,000、Indirect Cost: ¥1,800,000); Fiscal Year 2011: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000); Fiscal Year 2010: ¥7,800,000 (Direct Cost: ¥6,000,000、Indirect Cost: ¥1,800,000); Fiscal Year 2009: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000); Fiscal Year 2008: ¥8,840,000 (Direct Cost: ¥6,800,000、Indirect Cost: ¥2,040,000)
• Keywords: 代数解析 / 表現論 / 常微分方程式 / Kac-Moodyルート系 / 国際研究者交流 / 多国籍 / モノドロミー / 接続係数 / 積分幾何 / ルート系 / 超幾何関数 / 等質空間 / 確定特異点 / 特殊関数

Research Abstract

We established a general theory which analyzes the connection problem, the expression of solutions etc. of Fuchsian linear ordinary differential equations and got many new explicit results. We also gave a similar study for the equations which may have irregular singularities. Moreover we applied some results to problems in an integral geometry including Poisson transformations.

Research Products

• [Journal Article] An elementary approach to the Gauss hypergeometric function (2013)
  • Author(s): Toshio Oshima
  • Journal Title: Josai Mathematical Monograph Volume: 6 Pages: 3-23
  • NAID: 120005520752
  • Peer Reviewed
• [Journal Article] Classification of Fuchsian systems and their connection problem (2013)
  • Author(s): Toshio Oshima
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B37 Pages: 163-192
  • Peer Reviewed
• [Journal Article] An elementary approach to the Gauss hypergeometric function (2013)
  • Author(s): Toshio Oshima
  • Journal Title: Josai Mathematical Monographs Volume: 6 Pages: 3-23
  • NAID: 120005520752
  • Peer Reviewed
• [Journal Article] A classification of roots of symmetric Kac-Moody root systems and its application (2012)
  • Author(s): Kazuki Hiroe and Toshio Oshima
  • Journal Title: Springer Proceedings in Mathematics and Statistics Volume: 40 Pages: 195-241
  • Peer Reviewed
• [Journal Article] A classification of roots of symmetric Kac-Moody root systems and its application (2012)
  • Author(s): Kazuki Hiroe
  • Journal Title: Symmetries, Integrable Systems and Representations, Springer Proceedings in Mathematics and Statistics Volume: 40 Pages: 195-241
  • Peer Reviewed
• [Journal Article] Fractional calculus of Weyl algebra and Fuchsian differential equations (2011)
  • Author(s): T.Oshima
  • Journal Title: UTMS 2011-5 Pages: 1-194
• [Journal Article] Boundary value problems on Riemannian symmetric spaces of the noncompact Type (2011)
  • Author(s): T.Oshima, N.Shimeno
  • Journal Title: UTMS 2011-4 Pages: 1-26
• [Journal Article] Boundary value problems on Riemannian symmetric spaces of the noncompact Type (2011)
  • Author(s): T.Oshima, N.Shimeno
  • Journal Title: UTMS Volume: 2011-4 Pages: 1-26
• [Journal Article] Fractional calculus of Weyl algebra and Fuchsian differential equations (2011)
  • Author(s): T.Oshima
  • Journal Title: UTMS Volume: 2011-5 Pages: 1-194
• [Journal Article] Heckman-Opdam hypergeometric functions and their specializations (2010)
  • Author(s): Toshio Oshima and Nobukazu Shimeno
  • Journal Title: RIMS Kokyuroku Bessatsu B Volume: 20 Pages: 129-162
  • Peer Reviewed
• [Journal Article] Heckman-0pdam hypergeometric functions and their specializations (2010)
  • Author(s): T.Oshima, N.Shimeno
  • Journal Title: RIMS Kokyuroku Bessatsu Pages: 129-162
  • Peer Reviewed
• [Journal Article] Heckman-Opdam hypergeometric functions and their specializations (2010)
  • Author(s): T.Oshima, N.Shimeno
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B20 Pages: 129-162
  • Peer Reviewed
• [Presentation] Riemann球面上の代数的線型常微分方程式 (2012)
  • Author(s): 大島利雄
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京理科大
  • Year and Date: 2012-03-28
• [Presentation] Ordinary differential equations and Kac-Moody root systems (2012)
  • Author(s): Toshio Oshima
  • Organizer: Conference - Lie groups: structure, actions and representations
  • Place of Presentation: Bochum, ドイツ
  • Year and Date: 2012-01-12
• [Presentation] Generalizations of Radon transforms on compact homogeneous spaces, Tufts University (2012)
  • Author(s): Toshio Oshima
  • Organizer: Geometric Analysis on Euclidean and Homogeneous Spaces
  • Place of Presentation: Tufts University, アメリカ
  • Year and Date: 2012-01-08
• [Presentation] Linear differential equations on the Riemann sphere and special functions (2012)
  • Author(s): Toshio Oshima
  • Organizer: Seminar on Representation Theory
  • Place of Presentation: Amsterdam 大学, オランダ
  • Invited
• [Presentation] 多項式係数の線型常微分方程式と特殊関数 (2012)
  • Author(s): 大島利雄
  • Organizer: 微分方程式の総合的研究，サーベイ講演
  • Place of Presentation: 京都大学理学部
  • Invited
• [Presentation] 常微分方程式と特殊関数の計算 (2011)
  • Author(s): 大島利雄
  • Organizer: 計算による数理科学の展開
  • Place of Presentation: 神戸大学
  • Year and Date: 2011-01-08
• [Presentation] Fuchs型方程式の合流と分岐を持たない不確定特異点を許す方程式とKac--Moodyルート系 (2011)
  • Author(s): 大島利雄
  • Organizer: Workshop on Accessory Parameters
  • Place of Presentation: 東京大学玉原国際セミナーハウス，沼田
• [Presentation] Fuchs型常微分方程式とKac-Moody root系 (2010)
  • Author(s): 大島利雄
  • Organizer: 2010年表現論シンポジウム
  • Place of Presentation: 伊豆長岡
  • Year and Date: 2010-11-11
• [Presentation] 特異点の合流とmiddle convolution (2010)
  • Author(s): 大島利雄
  • Organizer: Workshop on Accessory Parameters
  • Place of Presentation: 玉原国際セミナーハウス
  • Year and Date: 2010-10-12
• [Presentation] Gauss超幾何の初等的解析 (2010)
  • Author(s): 大島利雄
  • Organizer: Workshop on Accessory Parameters
  • Place of Presentation: 玉原国際セミナーハウス
  • Year and Date: 2010-10-10
• [Presentation] 数式処理(risalasir)とTeXとdviout (2010)
  • Author(s): 大島利雄
  • Organizer: ポスター発表 TeXユーザの集い
  • Place of Presentation: 生産技術研究所 東京大学
  • Year and Date: 2010-09-30
• [Presentation] Boundary value Problems for Riemannian symmetric spaces (2010)
  • Author(s): 大島利雄
  • Organizer: Special lecture
  • Place of Presentation: 東北師範大学,長春,中国
  • Year and Date: 2010-06-09
• [Presentation] Boundary value problems for Riemannian symmetric spaces (2010)
  • Author(s): 大島利雄
  • Organizer: Special lecture
  • Place of Presentation: 東北師範大学 長春 中国
  • Year and Date: 2010-06-09
• [Presentation] Kac-Moody root systems and linear algebraic differential equations (2010)
  • Author(s): 大島利雄
  • Organizer: International workshop on representation theory and harmonic analysis
  • Place of Presentation: 南開研究所,中国
  • Year and Date: 2010-06-07
• [Presentation] Kac-Moody root systems and linear algebraic differential equations (2010)
  • Author(s): 大島利雄
  • Organizer: International workshop on representation theory and harmonic analysis
  • Place of Presentation: 南開研究所 中国
  • Year and Date: 2010-06-07
• [Presentation] 特殊関数と代数的線形常微分方程式 (2010)
  • Author(s): 大島利雄
  • Organizer: 日本数学会企画特別講演
  • Place of Presentation: 慶應大学
  • Year and Date: 2010-03-27
• [Presentation] 特殊関数と代数的線形常微分方程式 (2010)
  • Author(s): 大島利雄
  • Organizer: 日本数学会企画特別講演
  • Place of Presentation: 慶応大学
  • Year and Date: 2010-03-27
• [Presentation] Fuchs型方程式の解析-部分Wronskianの間の接続係数 (2010)
  • Author(s): 大島利雄
  • Organizer: アクセサリー・パラメーター研究会
  • Place of Presentation: 熊本大学
  • Year and Date: 2010-03-18
• [Presentation] Fuchs型方程式の解析-rigidな系列を例にとって (2010)
  • Author(s): 大島利雄
  • Organizer: アクセサリー・パラメーター研究会
  • Place of Presentation: 熊本大学
  • Year and Date: 2010-03-17
• [Presentation] Universal model of Fuchian differential equations (2010)
  • Author(s): 大島利雄
  • Organizer: 超幾何方程式研究会 2010
  • Place of Presentation: 神戸大学
  • Year and Date: 2010-01-07
• [Presentation] 連続講演"スペクトルタイプからみたFuchs型微分方程式" (2010)
  • Author(s): 大島利雄
  • Organizer: 常微分方程式ミニ研究会
  • Place of Presentation: 九州大学
• [Presentation] 連続講演"Fuchs型常微分方程式についての最近の結果の概説" (2010)
  • Author(s): 大島利雄
  • Organizer: Workshop on Accessory Parameters
  • Place of Presentation: 玉原国際セミナーハウス
• [Presentation] Fractional calculus of Weyl algebra and its applications (2009)
  • Author(s): 大島利雄
  • 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: 2009-08-08
• [Presentation] Fractional calculus of Weyl algebra and its applications (2009)
  • Author(s): 大島利雄
  • Organizer: Representation Theory of Real Reductive Groups
  • Place of Presentation: The University of Uta
  • Year and Date: 2009-07-30
• [Presentation] Fractional calculus of Weyl algebra and its applications I, II (2009)
  • Author(s): 大島利雄
  • Organizer: Workshop on Accessory Parameters
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2009-06-21
• [Presentation] Fractional calculus of Weyl algebra and its applications (2009)
  • Author(s): 大島利雄
  • Organizer: 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: 2009-06-04
• [Presentation] 旗多様体を規定する微分方程式 (2009)
  • Author(s): 大島利雄
  • Organizer: 第50回ラドン変換--積分が拓く新しい世界--, Encounter with Mathematics
  • Place of Presentation: 中央大学
  • Year and Date: 2009-05-30
• [Presentation] 旗多様体を規定する微分方程式,第50回ラドン変換-積分が拓く新しい世界- (2009)
  • Author(s): 大島利雄
  • Organizer: Encounter with Mathematics
  • Place of Presentation: 中央大学
  • Year and Date: 2009-03-30
• [Presentation] (偏)微分作用素の middle convolution (2009)
  • Author(s): 大島利雄
  • Organizer: Workshop on Accessory Parameters at Kumamoto
  • Place of Presentation: 熊本大学
  • Year and Date: 2009-02-21
• [Presentation] Fuchs 型常微分方程式と Kac-Moody ルート系 (2008)
  • Author(s): 大島利雄
  • Organizer: 2008年度表現論ワークショップ
  • Place of Presentation: とりぎん文化会館
  • Year and Date: 2008-12-26
• [Presentation] Heckman-Opdam hypergeometric functions and their specializations (2008)
  • Author(s): 大島利雄
  • Organizer: 研究集会:表現論と非可換調和解析における新しい視点
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-09-18
• [Presentation] On Fuchsian systems --classification, connection problems and Kac-Moody Lie algebra-- (2008)
  • Author(s): 大島利雄
  • Organizer: 日露表現論ワークショップ
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2008-08-29
• [Presentation] 特別講演:分かる Fuchs 型常微分方程式 (2008)
  • Author(s): 大島利雄
  • Organizer: 第47回実函数論函数解析学合同シンポジウム
  • Place of Presentation: 慶応大学矢上キャンパス
  • Year and Date: 2008-08-07
• [Presentation] Fuchs 型方程式の可約性と接続公式 (2008)
  • Author(s): 大島利雄
  • Organizer: Workshop on accessory parameters
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2008-08-05
• [Presentation] Middle convolution の組み合わせ論的側面 (2008)
  • Author(s): 大島利雄
  • Organizer: Workshop on accessory parameters
  • Place of Presentation: 東京大学玉原国際セミナーハウス
  • Year and Date: 2008-08-04
• [Presentation] モジュライのない Fuchs 型常微分方程 (2008)
  • Author(s): 大島利雄
  • Organizer: 研究集会:完全WKB解析と超局所解
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-05-26
• [Presentation] Radon transforms on compact manifolds
  • Author(s): Toshio Oshima
  • Organizer: Representation Theory and Harmonic Analysis
  • Place of Presentation: Chern Institute of Mathematics, Nankai University, China
  • Invited
• [Presentation] Linear differential equations on the Riemann sphere
  • Author(s): Toshio Oshima
  • Organizer: 超幾何関数とその周辺
  • Place of Presentation: 東京大学玉原国際セミナーハウス，沼田
• [Presentation] Dynkin図式と常微分方程式
  • Author(s): 大島利雄
  • Organizer: 幾何学とインターネット数理
  • Place of Presentation: 東京大学玉原国際セミナーハウス，沼田
• [Presentation] 微分作用素の計算への応用を見込んだRisa/Asir入門
  • Author(s): 大島利雄
  • Organizer: アクセサリー・パラメーター研究会
  • Place of Presentation: 東京大学玉原国際セミナーハウス，沼田
• [Presentation] 常微分作用素環における単因子論
  • Author(s): 大島利雄
  • Organizer: Representation theory of algebraic groups and representation theory
  • Place of Presentation: 都市センターホール，東京
• [Presentation] Linear differential equations on the Riemann sphere
  • Author(s): Toshio Oshima
  • Organizer: Various Aspects on the Painleve Equations
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] 2変数多項式の分類
  • Author(s): 大島利雄
  • Organizer: 2012年度表現論ワークショップ
  • Place of Presentation: 県民ふれあい会館, 鳥取
• [Presentation] 2次元シンプレクティック・ベクトル空間内の代数曲線に対する Deligne-Simpson問題
  • Author(s): 大島利雄
  • Organizer: 代数幾何講演会
  • Place of Presentation: 埼玉大学理学部
  • Invited
• [Presentation] 代数的線型常微分方程式の古典極限
  • Author(s): 大島利雄
  • Organizer: アクセサリー・パラメーター研究会
  • Place of Presentation: 熊本大学
• [Presentation] Ordinary differential equations and Kac-Moody root systems
  • Author(s): Toshio Oshima
  • Organizer: Recent Developments in Harmonic Analysis and their Applications
  • Place of Presentation: Marrakech, Morocco
  • Invited
• [Presentation] Boundary value problems on Riemannian symmetirc spaces and minimal polynomials associated to generalized Verma modules
  • Author(s): Toshio Oshima
  • Organizer: International Workshop on Representation Theory and Harmonic Analysis
  • Place of Presentation: Chern Institute of Mathematics, Nankai University, China
  • Invited
• [Presentation] 代数的線形常微分方程式とKac--Moodyルート系
  • Author(s): 大島利雄
  • Organizer: 2011年度表現論シンポジウム
  • Place of Presentation: みなべ町，和歌山
  • Invited
• [Presentation] Radon変換の一般化について
  • Author(s): 大島利雄
  • Organizer: 表現論Workshop 2011
  • Place of Presentation: 鳥取市
• [Presentation] Generalizations of Radon transforms on compact homogeneous spaces
  • Author(s): Toshio Oshima
  • Organizer: Geometric Analysis on Euclidean and Homogeneous Spaces
  • Place of Presentation: Tufts Universitry, USA
  • Invited
• [Presentation] Ordinary differential equations and Kac-Moody root systems
  • Author(s): Toshio Oshima
  • Organizer: Conference - Lie groups: structure, actions and representations
  • Place of Presentation: Bochum, Germany
  • Invited
• [Presentation] 常微分作用素のスペクトル型とuniversal unfolding model
  • Author(s): 大島利雄
  • Organizer: アクセサリー・パラメーター研究会
  • Place of Presentation: 熊本大学
• [Presentation] Riemann球面上の代数的線型常微分方程式
  • Author(s): 大島利雄
  • Organizer: 日本数学会年会，特別講演
  • Place of Presentation: 東京理科大学
  • Invited
• [Book] Fractional calculus of Weyl algebra and Fuchsian differential equations, MSJ Memoirs 28 (2012)
  • Author(s): Toshio Oshima
  • Total Pages: 203
  • Publisher: 日本数学会
• [Book] MSJ Memoirs 28, 日本数学会 (2012)
  • Author(s): Toshio Oshima
  • Total Pages: 203
  • Publisher: Fractional calculus of Weyl algebra and Fuchsian differential equations
• [Book] 特殊関数と代数的線型常微分方程式,東京大学数理科学レクチャーノート11 (2011)
  • Author(s): 大島利雄
  • Total Pages: 111
  • Publisher: 東京大学数理科学研究科
  • URL: http://www.ms.u-tokyo.ac.jp/publication/lecturenote.html
• [Book] 特殊関数と代数的線型常微分方程式 (2011)
  • Author(s): 大島利雄
  • Total Pages: 111
  • Publisher: 東京大学数理科学レクチャーノート
• [Book]
  • Author(s): http://akagi.ms.u-tokyo.ac.jp/oshima
• [Remarks]
  • URL: http://akagi.ms.u-tokyo.ac.jp/~oshima
• [Remarks] ホームページ
  • URL: http://akagi.ms.u-tokyo.ac.jp/~oshima
• [Remarks]
  • URL: http://akagi.ms.u-tokyo.ac.jp/~oshima
• [Remarks]
  • URL: http://akagi.ms.u-tokyo.ac.jp/~oshima