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Orbit decomposition of multiple flag varieties

Research Project

Project/Area Number 25400030
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionRyukoku University

Principal Investigator

Matsuki Toshihiko  龍谷大学, 文学部, 教授 (20157283)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords古典群 / 代数群 / 旗多様体
Outline of Final Research Achievements

For a multiple flag variety (a direct product of flag varieties) of split orthogonal groups of odd degree over an infinite field of characteristic not two, we gave the necessary and sufficient condition for the finiteness of G-orbits under the diagonal action. For general linear groups and symplectic groups (over an algebraically closed fields), the conditions were given by Magyar-Weyman-Zelevinsky. It seems we can also solve the even-degree case by the same method.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (9 results)

All 2016 2015 2014 2013 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results,  Acknowledgement Compliant: 1 results) Presentation (6 results) (of which Int'l Joint Research: 1 results,  Invited: 2 results) Remarks (2 results)

  • [Journal Article] Orthogonal multiple flag varieties of finite type I: Odd degree case2015

    • Author(s)
      Toshihiko Matsuki
    • Journal Title

      Journal of Algebra

      Volume: 425 Pages: 450-523

    • DOI

      10.1016/j.jalgebra.2014.11.016

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Orthogonal multiple flag varieties2016

    • Author(s)
      Toshihiko Matsuki
    • Organizer
      Sphericity 2016
    • Place of Presentation
      Kloster Reute, Germany
    • Year and Date
      2016-02-22
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 奇数次直交群の有限型多重旗多様体の分類2014

    • Author(s)
      松木敏彦
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 奇数次直交群の3重旗多様体の軌道分解2014

    • Author(s)
      松木敏彦
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 奇数次直交群の有限型多重旗多様体2014

    • Author(s)
      松木敏彦
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-06-24 – 2014-06-27
    • Related Report
      2014 Research-status Report
  • [Presentation] Group actions on multiple flag varieties2014

    • Author(s)
      T. Matsuki
    • Organizer
      Spring school for Representation theory and geometry of reductive groups
    • Place of Presentation
      Kloster Heiligkreuztal, Germany
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 直交群の多重旗多様体の有限型軌道分解2013

    • Author(s)
      松木敏彦
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks] Home page of Toshihiko MATSUKI (松木敏彦)

    • URL

      http://www.ab.auone-net.jp/~matsuki/

    • Related Report
      2014 Research-status Report
  • [Remarks] Home page of Toshihiko MATSUKI (松木敏彦)

    • URL

      http://www.ab.auone-net.jp/~matsuki/

    • Related Report
      2013 Research-status Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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