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A classification of reductive prehomogeneous vector spaces and its application

Research Project

Project/Area Number 18540010
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionUniversity of Tsukuba

Principal Investigator

KIMURA Tatsuo  University of Tsukuba, 大学院・数理物質科学研究科, 教授 (30022726)

Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,150,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥750,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Keywords代数一般 / 概均質ベクトル空間 / 簡約可能代数群 / 分類 / クイバー
Research Abstract

We classified some prehomogeneous vector spaces (abbrev.PV) and as its application, we completed the classification of irreducible weakly spherical homogeneous spaces. The form of some of relative invariants of 2-simple PVs of type I were not known and we gave them explicitly. Then we classified some finite PVs including various scalar multiplications from which hypergeometric functions arise. We also develop the results of classification of reductive PVs by M.Sato.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (26 results)

All 2011 2010 2009 2008 2007 2006

All Journal Article (12 results) (of which Peer Reviewed: 10 results) Presentation (9 results) Book (5 results)

  • [Journal Article] On M. Sato's classification of some reductive prehomogeneous vector spaces2011

    • Author(s)
      T. Kimura, Y. Ishii, I. Ryu, M. Hamada, Y. Kurosawa, M. Ouchi, T. Kamiyoshi
    • Journal Title

      Publ.of R.I.M.S. (to appear)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On M.Sato's classification of some reductive prehomogeneous vector spaces2010

    • Author(s)
      木村達雄、石井、柳、濱田、黒澤、大内、神吉
    • Journal Title

      Publication of R.I.M.S. (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A classification of representations ρ(×)Λ_1 of reductive algebraic group G×SL(n) with finitely many orbits2008

    • Author(s)
      T. Kimura, T. Kamiyoshi, N. Maki, M. Ouchi, M. Takano
    • Journal Title

      AGG vol. 25

      Pages: 115-159

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A classification of representations ρ[○!×]Λ_1 of reductive algebraic groups G×SLn (n≧2) with finitely many orbits2008

    • Author(s)
      T. Kimura, T. Kamiyoshi, N. Maki, M. Ouchi and M.Takano
    • Journal Title

      A. G. G vol 25

      Pages: 115-160

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A classification of representations p 〓 1 of reductive algebraic groups G x SLn (n ≧ 2) with finitely many orbits,2008

    • Author(s)
      木村達雄、神吉知博、牧徳達、大内将也、高野みずほ
    • Journal Title

      ALGEBRAS GROUPS AND GEOMETRIES 25

      Pages: 115-160

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relative invariants of 2-simple prehomogeneous vector spaces of type I2007

    • Author(s)
      T. Kimura, T. Kogiso, K. Sugiyama
    • Journal Title

      J.Algebra vol. 308

      Pages: 445-483

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relative invariants of 2-simple prehomogeneous vector spaces of type I2007

    • Author(s)
      T. Kimura, T. Kogiso and K. Sugiyama
    • Journal Title

      J. Algebra vol. 308

      Pages: 445-483

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Relative invariants of 2-simple prehomogeneous vector spaces of type I2007

    • Author(s)
      木村達雄、小木曽岳義、杉山和成
    • Journal Title

      Journal of Algebra 308

      Pages: 445-483

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relative invariants of 2-simple prehomogeneous vector spaces of type I2007

    • Author(s)
      木村達雄, 小木曽岳義, 杉山和成
    • Journal Title

      Journal of Algebra 308

      Pages: 445-483

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A classification of irreducible weakly spherical homogeneous spaces2006

    • Author(s)
      T. Kimura, D. Takeda, T. Kamiyoshi
    • Journal Title

      J.Algebra vol. 302

      Pages: 793-816

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A classification of irreducible weakly spherical homogeneous spaces2006

    • Author(s)
      T. Kimura, D. Takeda and T. Kamiyoshi
    • Journal Title

      J. Algebra vol. 302

      Pages: 445-483

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A classification of irreducible weakly spherical homogeneous spaces2006

    • Author(s)
      木村達雄, 竹田大佑, 神吉知博
    • Journal Title

      Journal of Algebra 302

      Pages: 793-816

    • Related Report
      2006 Annual Research Report
  • [Presentation] 佐藤幹夫先生による簡約可能概均質ベクトル空間の分類とその後の発展2009

    • Author(s)
      木村達雄
    • Organizer
      「簡約可能概均質ベクトル空間の分類とその応用」研究集会
    • Place of Presentation
      くば国際会議場 小会議室401
    • Year and Date
      2009-11-22
    • Related Report
      2009 Final Research Report
  • [Presentation] 佐藤幹夫先生による簡約可能概均質ベクトル空間の分類とその後の発展2009

    • Author(s)
      木村達雄
    • Organizer
      「簡約可能概均質ベクトル空間の分類とその応用」研究集会
    • Place of Presentation
      つくば国際会議場小会議室401
    • Year and Date
      2009-11-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] 笠井―黒澤による研究の補足2009

    • Author(s)
      木村達雄
    • Organizer
      「簡約可能概均質ベクトル空間の分類とその応用」研究集会
    • Place of Presentation
      つくば国際会議場 小会議室401
    • Year and Date
      2009-11-21
    • Related Report
      2009 Final Research Report
  • [Presentation] 笠井-黒澤による研究の補足2009

    • Author(s)
      木村達雄
    • Organizer
      「簡約可能概均質ベクトル空間の分類とその応用」研究集会
    • Place of Presentation
      つくば国際会議場小会議室401
    • Year and Date
      2009-11-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] 簡約可能概均質ベクトル空間の分類の現状2008

    • Author(s)
      木村達雄
    • Organizer
      「簡約可能概均質ベクトル空間の分類理論」研究集会
    • Place of Presentation
      つくば国際会議場 小会議室403
    • Year and Date
      2008-11-29
    • Related Report
      2009 Final Research Report
  • [Presentation] 簡約可能概均質ベクトル空間の分類の現状2008

    • Author(s)
      木村達雄
    • Organizer
      「簡約可能概均質ベクトル空間の分類理論」研究集会
    • Place of Presentation
      つくば国際会議場
    • Year and Date
      2008-11-29
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] 簡約可能概均質ベクトノレ空間の分類の現状2008

    • Author(s)
      木村達雄
    • Organizer
      「簡約可能概均質ベクトル空間の分類理論」研究集会
    • Place of Presentation
      つくば国際会議場
    • Year and Date
      2008-11-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] 有限軌道をもつ(G×GL(n)、ρ[○!×]Λ_1)(n≧2)の分類2008

    • Author(s)
      木村達雄、神吉知博、大内将也
    • Place of Presentation
      日本数学会、近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] 有限軌道をもつ(G×GL(n),ρ×Λ_1)(n≧2)の分類2008

    • Author(s)
      木村達雄、神吉知博、大内将也
    • Organizer
      日本数学会総会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2007 Annual Research Report
  • [Book] 代数の魅力2009

    • Author(s)
      木村達雄, 竹内光弘, 宮本雅彦, 森田純, 著
    • Publisher
      数学書房
    • Related Report
      2009 Final Research Report
  • [Book] 代数の魅力2009

    • Author(s)
      木村達雄(第一著者)
    • Total Pages
      227
    • Publisher
      数学書房
    • Related Report
      2009 Annual Research Report
  • [Book] 佐藤幹夫の数学2007

    • Author(s)
      木村達雄, 編
    • Total Pages
      376
    • Publisher
      日本評論社
    • Related Report
      2009 Final Research Report
  • [Book] 佐藤幹夫の数学2007

    • Author(s)
      木村達雄
    • Total Pages
      376
    • Publisher
      日本評論社
    • Related Report
      2008 Self-evaluation Report
  • [Book] 佐藤幹夫の数学2007

    • Author(s)
      木村達雄 編
    • Total Pages
      376
    • Publisher
      日本評論社
    • Related Report
      2007 Annual Research Report

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

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