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ANALYSIS ON INVARIANTS ASSOCIATED WITH PREHOMOGENEOUS VECTOR SPACES FROM THE VIEW POINT OF REPRESENTATION THEORY

Research Project

Project/Area Number 19740003
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionChiba Institute of Technology (2008-2009)
University of Tsukuba (2007)

Principal Investigator

SUGIYAMA Kazunari  Chiba Institute of Technology, 情報科学部, 助教 (90375395)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥2,360,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
Keywords概均質ベクトル空間 / クイバー / b-関数 / リー環 / ゼータ関数 / タイバー
Research Abstract

We have studied the b-functions of relative invariants of the prehomogeneous vector spaces associated with quivers of type A. By applying the decomposition formula for b-functions, we determine explicitly the b-functions of one-variable for each irreducible relative invariant. Moreover, we give a graphical algorithm to determine the b-functions of several variables. As its application, we have obtained some results on functional equations of prehomogeneous vector spaces of parabolic type arising from special linear Lie algebras.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (11 results)

All 2010 2009 2008 2007

All Journal Article (5 results) (of which Peer Reviewed: 4 results) Presentation (6 results)

  • [Journal Article] b-Functions and representation theory of quivers2010

    • Author(s)
      杉山和成
    • Journal Title

      数理解析研究所講究録別冊 (掲載決定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] b-Functions and the representation theory of quivers2010

    • Author(s)
      Kazunari Sugiyama
    • Journal Title

      数理解析研究所講究録別冊 掲載決定

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A型の箙に付随するb-関数について2008

    • Author(s)
      杉山和成
    • Journal Title

      2008年度表現論シンポジウム報告集

      Pages: 67-79

    • NAID

      130008004855

    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [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 No.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, K., Sugiyama
    • Journal Title

      Journal of Algebra 308

      Pages: 445-483

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] 特殊線形リー環から現れる放物型概均質ベクトル空間のフーリエ変換について2009

    • Author(s)
      杉山和成
    • Organizer
      研究集会「概均質ベクトル空間論の最近の展開」
    • Place of Presentation
      九州大学
    • Year and Date
      2009-12-23
    • Related Report
      2009 Final Research Report
  • [Presentation] A型の箙に付随するb-関数について2009

    • Author(s)
      杉山和成
    • 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
      2009-06-01
    • Related Report
      2009 Final Research Report
  • [Presentation] A型の箙に付随するb-関数について2009

    • Author(s)
      杉山和成
    • 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(京都府)
    • Year and Date
      2009-06-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] A型の箙に付随するb-関数について2008

    • Author(s)
      杉山和成
    • Organizer
      2008年度表現論シンポジウム
    • Place of Presentation
      ウェルハートピア熱海
    • Year and Date
      2008-11-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] A型の箙に付随するb-関数について2008

    • Author(s)
      杉山和成
    • Organizer
      2008年度日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2009 Final Research Report
  • [Presentation] A型の腹の表現に付随するb -関数について2008

    • Author(s)
      杉山和成
    • Organizer
      2008年日本数学会年会
    • Place of Presentation
      近畿大学理工学部
    • Year and Date
      2008-03-24
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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