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Research on monoids consisting of limits of linear actions on a projective manifold

Research Project

Project/Area Number 15K13421
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionHokkaido University

Principal Investigator

SAITO Mutsumi  北海道大学, 理学研究院, 教授 (70215565)

Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords代数半群 / 線型代数半群 / コンパクト化 / 超幾何微分方程式系
Outline of Final Research Achievements

As a compactification of the projective linear group PGL(V), I have proposed PM(V). It is a compact topological space including PGL(V) as a dense open subset, and it is a monoid acting on the projective space P(V). In addition, I have related it to the well-known compactification -- the wonderful compactification of PGL(V).
In collaboration with Hiroyasu Takeda, I have made a description of the process of confluence of hypergeometric systems a la Gel’fand, as a limit under the adjoint action of a principal nilpotent p-tuple generalizing a principal nilpotent element.

Academic Significance and Societal Importance of the Research Achievements

PGL(V)のコンパクト化として良く知られたワンダフルコンパクト化は,半群ではなく,射影空間P(V)に作用できない。従って,射影空間P(V)に作用できるコンパクトな半群であるPM(V)は学術的意義があり,今後の応用が期待される。
ゲルファント流超幾何微分方程式系は,そのパラメータ空間の双対が,一般線型リー代数の正則元の中心化代数となるものが今まで知られていたが,より一般な主冪零p組の中心化代数となるものを確定特異点型からの変形を含めて考察したことに意義がある。

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (4 results)

All 2018 2017 2015

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Open Access: 1 results) Presentation (2 results) (of which Invited: 1 results)

  • [Journal Article] Confluent hypergeometric systems associated with principal nilpotent p-tuples2018

    • Author(s)
      Mutsumi Saito, Hiroyasu Takeda
    • Journal Title

      International Journal of Mathematics

      Volume: 29 Issue: 12 Pages: 1850079-1850079

    • DOI

      10.1142/s0129167x18500799

    • NAID

      120006734167

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Limits of Jordan Lie subalgebras2017

    • Author(s)
      Mutsumi Saito
    • Journal Title

      Journal of Lie Theory

      Volume: 27 Pages: 51-84

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Presentation] PGL(V)の或るコンパクト化について2017

    • Author(s)
      齋藤睦
    • Organizer
      第5回半田山・幾何・代数セミナー
    • Related Report
      2017 Research-status Report
  • [Presentation] Jordan Lie 部分代数の変形2015

    • Author(s)
      齋藤睦
    • Organizer
      RIMS研究集会「幾何学・組合せ論に現れる環と代数構造」
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2015-06-12
    • Related Report
      2015 Research-status Report
    • Invited

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Published: 2015-04-16   Modified: 2020-03-30  

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