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Study on prehomogeneous vector spaces

Research Project

Project/Area Number 09640029
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

MATSUKI Toshihiko (1998)  Kyoto Univ., Integrated Human Studies, Ass. Professor, 総合人間学部, 助教授 (20157283)

行者 明彦 (1997)  京都大学, 総合人間学部, 助教授 (50116026)

Co-Investigator(Kenkyū-buntansha) SAITO Hiroshi  Kyoto Univ., Graduate School of Human and Environmental Studies, Professor, 大学院・人間・環境研究科, 教授 (20025464)
HIOKI Hirohisa  Kyoto Univ., Integrated Human Studies, Assistant, 総合人間学部, 助手 (70293842)
UEDA Tetsuo  Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (10127053)
KONO Norio  Kyoto Univ., Integrated Human Studies, Professor, 総合人間学部, 教授 (90028134)
KATO Shinichi  Kyoto Univ., Integrated Human Studies, Ass. Professor, 総合人間学部, 助教授 (90114438)
松木 敏彦  京都大学, 総合人間学部, 助教授 (20157283)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1998: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1997: ¥1,900,000 (Direct Cost: ¥1,900,000)
Keywordsprehomogeneous vector space / zeta function / Lie group / algebraic group / homogeneous space / リー群 / ヘッケ環 / 球関数 / 対称空間 / 軌道分解 / 進化ゲノム理論 / 動的パターン投影法
Research Abstract

First, we studied double coset decompositions of compact Lie groups with respect to two symmetric subgroups. We got a precise decomposition theorem, classification and a theory of root systems. We also computed orbit structure on flag manifolds under the action of some typical spherical subgroups.
Secondly, we studied zeta functions on reduced prehomogeneous vector spaces. We showed the convergence of the zeta function under the condition that the isotropy subgroup contains no 2-dimensional torus. We also gave the functional equation for the zeta function on archimedian fields with respect to the prehomogeneous vector space no. 15 in the sense of Kimura-Sato.
Thirdly, we studied p-adic spherical homogeneous spaces. We gave the orbit decomposition and got the uniqueness and an explicit formula of the spherical functions under some comditions.
We also studied complex dynamical system over projective spaces and a computational pattern projection method to handle dynamical three-dimensional scenes.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report

Research Products

(24 results)

All Other

All Publications (24 results)

  • [Publications] 松木敏彦: "Classitication of two involutions on compact semisimple Lie groups and root systems" 未定. (未定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 河野 敬雄: "How big are the increments of a two-parameter Gaussian process?" J.Theoretical Probability. 12・1. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 河野 敬雄: "On tail probability of local times of Gaussian processes." J.Stochastic Processes and their Applications. (未定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 齋藤, 裕: "On zeta functions associated to symmetric matricesII: Functional equations and special values." 未定. (未定). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 齋藤, 裕: "Explicit form of Zeta functions of Prehomogeneous Vector Spaces" Math.Ann.(未定). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 上田 哲生: "Critically finite maps on projective Spaces" The Journal of Geometric Analysis. (未定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T,Matsuki: "Classification of two involutions on compact Semisimple Liegroups and root systems." (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Kono: "How big are the increments of a two-parameter Gaussian process?" J.Theoretical Probability. Vol.12. No.1 (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Kono: "On tail probability of local times of Gaussian Processes" J.Stochastic Processes and their Applications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Saito: "On zeta functions associated to symmetric matrices II : Functional equations and special values." (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Saito: "Explicit form of zeta functions of prehomogeneous vector spaces" Math. Ann. (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Ueda: "Critically finite maps on projective spaces" the Journal of Geometric Analysis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 松木敏彦: "Classification of two involutions on compact semisimple Lie groups and root systems"

    • Related Report
      1998 Annual Research Report
  • [Publications] 河野敬雄: "How big are the increments of a two-parameter Gaussian process?" J.Theoretical Probability.12・1. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 河野敬雄: "On tail probability of local times of Gaussian Processes." J.Stochastic Processes and their Applications.

    • Related Report
      1998 Annual Research Report
  • [Publications] 斎藤裕: "On zeta functions associated to symmetric matrices II : Functional equations and special values." (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 斎藤裕: "Explicit form of zeta functions of Prehomogeneous Ve-ctor spaces" Math.Ann.(1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 上田哲生: "Critically finite maps on projective spaces" The Journal of Geometric Analysis.

    • Related Report
      1998 Annual Research Report
  • [Publications] 行者 明彦: "Recent development of the theory of prehomogeneous vector spaces" Sugaku Expositions. 10巻. 105-122 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 行者 明彦: "Theory of prehomogeneous vector spaces, II,a supplement" Pub1. RIMS. 33巻. 33-57 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 行者 明彦: "Character sums and intersection cohomology complexes associated to the space of square matrices" Indag. Math.8巻. 371-385 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 加藤 信一: "Hecke algebras and guantum general linear groups" J.Math, Kyoto Univ.37巻. 241-249 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 松木 敏彦: "Double coset decompositions of reductive Lie groups arising from two involutions" J.of Algebra. 197巻. 49-91 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 斉藤 裕: "Explicit formula of orbital p-adic zeta functions associated to symmetric and hermitian matrices" Comm. Math. Univ. St. Pauli. 46巻. 175-216 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-03-31   Modified: 2016-04-21  

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