A classification of reductive prehomogeneous vector spaces and its application

• Project/Area Number: 18540010
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: University 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: ¥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.

Research Products

• [Journal Article] On M. Sato's classification of some reductive prehomogeneous vector spaces (2011)
  • 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)
  • Peer Reviewed
• [Journal Article] On M.Sato's classification of some reductive prehomogeneous vector spaces (2010)
  • 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)
  • Peer Reviewed
• [Journal Article] A classification of representations ρ(×)Λ_1 of reductive algebraic group G×SL(n) with finitely many orbits (2008)
  • Author(s): T. Kimura, T. Kamiyoshi, N. Maki, M. Ouchi, M. Takano
  • Journal Title: AGG vol. 25 Pages: 115-159
  • Peer Reviewed
• [Journal Article] A classification of representations ρ[○!×]Λ_1 of reductive algebraic groups G×SLn (n≧2) with finitely many orbits (2008)
  • Author(s): T. Kimura, T. Kamiyoshi, N. Maki, M. Ouchi and M.Takano
  • Journal Title: A. G. G vol 25 Pages: 115-160
  • 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
  • Peer Reviewed
• [Journal Article] Relative invariants of 2-simple prehomogeneous vector spaces of type I (2007)
  • Author(s): T. Kimura, T. Kogiso, K. Sugiyama
  • Journal Title: J.Algebra vol. 308 Pages: 445-483
  • Peer Reviewed
• [Journal Article] Relative invariants of 2-simple prehomogeneous vector spaces of type I (2007)
  • Author(s): T. Kimura, T. Kogiso and K. Sugiyama
  • Journal Title: J. Algebra vol. 308 Pages: 445-483
  • Peer Reviewed
• [Journal Article] Relative invariants of 2-simple prehomogeneous vector spaces of type I (2007)
  • Author(s): 木村達雄、小木曽岳義、杉山和成
  • Journal Title: Journal of Algebra 308 Pages: 445-483
  • Peer Reviewed
• [Journal Article] Relative invariants of 2-simple prehomogeneous vector spaces of type I (2007)
  • Author(s): 木村達雄, 小木曽岳義, 杉山和成
  • Journal Title: Journal of Algebra 308 Pages: 445-483
• [Journal Article] A classification of irreducible weakly spherical homogeneous spaces (2006)
  • Author(s): T. Kimura, D. Takeda, T. Kamiyoshi
  • Journal Title: J.Algebra vol. 302 Pages: 793-816
  • Peer Reviewed
• [Journal Article] A classification of irreducible weakly spherical homogeneous spaces (2006)
  • Author(s): T. Kimura, D. Takeda and T. Kamiyoshi
  • Journal Title: J. Algebra vol. 302 Pages: 445-483
  • Peer Reviewed
• [Journal Article] A classification of irreducible weakly spherical homogeneous spaces (2006)
  • Author(s): 木村達雄, 竹田大佑, 神吉知博
  • Journal Title: Journal of Algebra 302 Pages: 793-816
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [Book] 佐藤幹夫の数学 (2007)
  • Author(s): 木村達雄
  • Total Pages: 376
  • Publisher: 日本評論社
• [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