• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Multiple flag varieties and exotic nilpotent varieties

Research Project

Project/Area Number 16K05070
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionAoyama Gakuin University

Principal Investigator

Nishiyama Kyo  青山学院大学, 理工学部, 教授 (70183085)

Project Period (FY) 2016-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords旗多様体 (Flag varieties) / 二重旗多様体 / 対称部分群 / 組合せ論 (Combinatorics) / スタインバーグ写像 / ヘッケ環 (Hecke algebras) / 冪零多様体 / RSK対応 / 多重旗多様体 / モーメント写像 / ヘッケ環 / 余法束多様体 / Steinberg理論 / グラスマン多様体 / exotic 冪零多様体 / 退化主系列表現 / exotic モーメント写像 / Robinson-Schensted 対応 / ゼータ積分 / Steinberg 多様体 / enhanced 隨伴作用 / ホロノミー図形 / enhanced 隨伴作用 / Riesz超関数 / conormal variety / moment map / flag variety / Springer correspondence / symmetric space
Outline of Final Research Achievements

Flag varieties are compact homogeneous spaces acted upon by a reductive Lie group, providing a broad field not only for the representation theory of Lie groups but also for the theories of geometry and algebra. In this research, we considered the product of flag varieties (double flag varieties) and studied the action of symmetric subgroups. Double flag varieties for which the orbits of symmetric subgroups are finite are called finite type. Various results were obtained in this research, including combinatorial aspects related to orbits on finite-type double flag varieties, representations of Hecke algebras, mappings to nilpotent varieties using moment maps, and the correspondence between orbits on double flag varieties and nilpotent orbits, known as the Steinberg correspondence, which is described combinatorially using a generalization of the RSK correspondence.

Academic Significance and Societal Importance of the Research Achievements

旗多様体は簡約リー群の作用するコンパクトな等質空間であって,リー群の表現論を始め,幾何学や代数学の理論に対しても幅広い舞台を提供している.本研究では旗多様体の直積(二重旗多様体)を考えて,対称部分群の作用を研究した.対称部分群の軌道が有限個であるような二重旗多様体は有限型と呼ばれる.有限型の二重旗多様体上の軌道にまつわる組合せ論やヘッケ環の表現,モーメント写像を用いた冪零多様体への写像,そしてスタインバーグ写像と呼ばれる二重旗多様体上の軌道と冪零軌道の対応,その組合せ論的記述であるRSK対応など様々な成果が本研究で得られた.

Report

(8 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (35 results)

All 2023 2022 2021 2020 2019 2018 2017 2016 Other

All Int'l Joint Research (1 results) Journal Article (8 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 6 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (22 results) (of which Int'l Joint Research: 13 results,  Invited: 16 results) Book (1 results) Remarks (3 results)

  • [Int'l Joint Research] IECL, ロレーヌ大学(フランス)

    • Related Report
      2020 Research-status Report
  • [Journal Article] On generalized Steinberg theory for type AIII2023

    • Author(s)
      Fresse Lucas、Nishiyama Kyo
    • Journal Title

      Algebraic Combinatorics

      Volume: 6 Issue: 1 Pages: 165-195

    • DOI

      10.5802/alco.245

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Orbit embedding for double flag varieties and Steinberg maps2021

    • Author(s)
      Fresse Lucas、Nishiyama Kyo
    • Journal Title

      Contemporary Mathematics

      Volume: 768 Pages: 21-42

    • DOI

      10.1090/conm/768/15451

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A Generalization of Steinberg Theory and an Exotic Moment Map2020

    • Author(s)
      Fresse Lucas、Nishiyama Kyo
    • Journal Title

      International Mathematics Research Notices

      Volume: 80 Issue: 1 Pages: 1-62

    • DOI

      10.1093/imrn/rnaa080

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Enhanced zeta distributions and its functional equations2019

    • Author(s)
      Nishiyama Kyo、Orsted Bent、Wachi Akihito
    • Journal Title

      Journal of Physics: Conference Series

      Volume: 1194 Pages: 012081-012081

    • DOI

      10.1088/1742-6596/1194/1/012081

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Enhanced adjoint actions and their orbits for the general linear group2019

    • Author(s)
      Nishiyama Kyo、Ohta Takuya
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 298 Issue: 1 Pages: 141-155

    • DOI

      10.2140/pjm.2019.298.141

    • Related Report
      2018 Research-status Report
  • [Journal Article] Real double flag varieties for the symplectic group2018

    • Author(s)
      Nishiyama Kyo、Orsted Bent
    • Journal Title

      Journal of Functional Analysis

      Volume: 274 Issue: 2 Pages: 573-604

    • DOI

      10.1016/j.jfa.2017.07.003

    • Related Report
      2018 Research-status Report 2017 Research-status Report
  • [Journal Article] CODIMENSION ONE CONNECTEDNESS OF THE GRAPH OF ASSOCIATED VARIETIES2016

    • Author(s)
      Kyo Nishiyama, Peter Trapa and Akihito Wachi
    • Journal Title

      Tohoku Mathematical Journal, Second Series

      Volume: 68 Issue: 2 Pages: 199-239

    • DOI

      10.2748/tmj/1466172770

    • NAID

      130008106072

    • ISSN
      0040-8735, 2186-585X
    • Year and Date
      2016-06-30
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the exotic Grassmannian and its nilpotent variety2016

    • Author(s)
      Lucas Fresse and Kyo Nishiyama
    • Journal Title

      Representation Theory

      Volume: 20 Issue: 16 Pages: 451-481

    • DOI

      10.1090/ert/489

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Hecke algebra actions on a double flag variety2022

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Representations and Characters: Revisiting the Works of Harish-Chandra and Andre Weil - A satellite conference of the virtual ICM 2022
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Hecke module structure on the orbits in double flag varieties2022

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Representation Theory XVII
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 二重旗多様体上の軌道とヘッケ環の表現2021

    • Author(s)
      西山享
    • Organizer
      第2回概均質ベクトル空間ミニワークショップ
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Steinberg theory for symmetric pairs2019

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Representation Theory XVI
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Robinson-Schensted Correspondence for Symmetric Pairs of Hermitian Tube Type2019

    • Author(s)
      Kyo Nishiyama
    • Organizer
      International Symposium on Addvances and Perspectives in Representation Theory
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] RSK correspondence and geometry2019

    • Author(s)
      Kyo Nishiyama
    • Organizer
      GCT Mini workshop
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] ある積分核作用素のフーリエ変換とその解析接続2019

    • Author(s)
      西山 享
    • Organizer
      第58回実函数論・函数解析学合同シンポジウム
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Steinberg 理論の一般化 (A型の場合)2019

    • Author(s)
      西山 享
    • Organizer
      日本数学会秋期総合分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] A 型対称対の exotic Robinson-Schensted 対応2019

    • Author(s)
      西山 享
    • Organizer
      日本数学会秋期総合分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] Robinson-Schensted Correspondence and Flag Varieties2019

    • Author(s)
      Kyo Nishiyama
    • Organizer
      MPI-INF and MPI-MiS joint workshop on Theoretical Computer Science and Algebraic Geometry
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Analytic continuation and Fourier transform of intertwiners between degenerate principal series2018

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Seminar on Lie groups and representation theory
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Functional equation of an enhanced zeta distribution2018

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Workshop "Dirac operators and representation theory"
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Fourier transform of the Riesz distribution on enhanced symmetric cone2018

    • Author(s)
      Kyo Nishiyama
    • Organizer
      The 32nd International Colloquium on Group Theoretical Methods in Physics (Group32)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Fourier transform of zeta integrals over enhanced positive cone2018

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Workshop on The Legacy of Joseph Fourier after 250 years, Dec.17-21, 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Integral kernel operators on tube domain associated with relative invariants2017

    • Author(s)
      Kyo Nishiyama
    • Organizer
      2017 Nankai Workshop on Representation Theory and Harmonic Analysis
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Integral kernel operators for degenerate principal series2017

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Representation Theory XV (Dubrovnik)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Moment map and nilpotent orbits2017

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Colloquium (Wuhan University)
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Enhanced adjoint action and its quotients2017

    • Author(s)
      西山 享
    • Organizer
      2017年度RIMS共同研究(公開型)「表現論と組合せ論」
    • Related Report
      2017 Research-status Report
  • [Presentation] Enhanced adjoint action and nilpotent variety2017

    • Author(s)
      西山享
    • Organizer
      農工大数学セミナー 2017
    • Place of Presentation
      東京農工大学小金井キャンパス 11 号館 1113 教室
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Intertwiners associated to a double flag variety over reals2016

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Workshop on Lie groups and representation theory
    • Place of Presentation
      Aarhus University, Denmark
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Intertwiners Between Degenerate Principal Series Arising From a Double Flag Variety2016

    • Author(s)
      Kyo Nishiyama
    • Organizer
      Harmonic Analysis on Lie Groups and Group Algebras of Locally Compact Groups
    • Place of Presentation
      TSIMF, Sanya, China
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] エルミート対称対の二重旗多様体と退化主系列表現2016

    • Author(s)
      西山享
    • Organizer
      2016年度表現論シンポジウム
    • Place of Presentation
      オキナワ グランメールリゾート(沖縄市与儀)
    • Related Report
      2016 Research-status Report
  • [Book] フリーズの数学 スケッチ帖2022

    • Author(s)
      西山 享
    • Total Pages
      312
    • Publisher
      共立出版
    • ISBN
      9784320114715
    • Related Report
      2022 Annual Research Report
  • [Remarks] WEB page (MATH/Research) : Kyo Nishiyama ; 西山 享

    • URL

      http://www.math.aoyama.ac.jp/users/kyo/index_math.html

    • Related Report
      2022 Annual Research Report
  • [Remarks] Web page of Kyo Nishiyama

    • URL

      http://www.math.aoyama.ac.jp/~kyo/index_math.html

    • Related Report
      2020 Research-status Report
  • [Remarks] WEB page (MATH/Research) : Kyo Nishiyama ; 西山 享

    • URL

      http://www.gem.aoyama.ac.jp/~kyo/index_math.html

    • Related Report
      2019 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi