Orbit correspondence on flag manifolds and integral transformations

• Project/Area Number: 19540076
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: MATSUKI Toshihiko Kyoto University, 大学院・理学研究科, 教授 (20157283)
• Co-Investigator(Kenkyū-buntansha): KIKUCHI Katsuhiko 京都大学, 大学院・理学研究科, 助教 (50283586)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 対称空間 / リー群 / 表現論

Research Abstract

We applied the horospherical Cauchy transformation due to S.Gindikin for the case of SU(2,1)/U(1,1). We compared the computer program to describe the orbits on flag manifolds with the description of subgroups of Weyl groups. We also computed examples of orbits on flag manifolds over finite fields by symmetric subgroups. We reduced the orbit decomposition of multiple flag varieties to smaller subgroups.

Research Products

• [Journal Article] The orbit correspondence on flag manifolds and the Stein extension of Riemannian symmetric spaces (2008)
  • Author(s): T. Matsuki
  • Journal Title: ugaku Expositions 21 Pages: 71-81
  • Peer Reviewed
• [Journal Article] Equivalence of domains arising from duality of orbits on flag manifolds III (2007)
  • Author(s): T. Matsuki
  • Journal Title: Trans. Amer. Math. Soc 359 Pages: 4773-4786
  • NAID: 120002511246
  • Peer Reviewed
• [Journal Article] Equivalence of domains arising from duality of orbits on flag manifolds III (2007)
  • Author(s): T. Matsuki
  • Journal Title: Trans. Amer. Math. Soc. 359 Pages: 4773-4786
  • NAID: 120002511246
  • Peer Reviewed
• [Journal Article] ジャーナリストの惨事ストレス(20)管理職の惨事ストレス経験と部下の日常ストレスへの対応
  • Author(s): 福岡欣治・井上果子・松井豊・安藤清志・畑中美穂
  • Journal Title: 日本トラウマティック・ストレス学会第9回大会総会プログラム・抄録集
• [Journal Article] 階数4のmultiplicity-free作用に関する不変式
  • Author(s): 菊地克彦
  • Journal Title: 数理解析研究所講究録別冊 (掲載予定)
  • Peer Reviewed
• [Presentation] 階数4の半古典型multiplicity-free作用に関する不変微分作用素 (2009)
  • Author(s): 菊地克彦
  • Organizer: 日本数学会年会
  • Year and Date: 2009-03-28
• [Presentation] Analysis and geometry on homogeneous spaces (2009)
  • Author(s): T. Matsuki
  • Organizer: 微分方程式と対称空間研究集会
  • Place of Presentation: 東大数理科学研究科
  • Year and Date: 2009-01-14
• [Presentation] 階数4のmultiplicity-free作用に関する不変式 (2008)
  • Author(s): 菊地克彦
  • Place of Presentation: 数理解析研究所研究集会
  • Year and Date: 2008-09-17
• [Presentation] Duality of orbits on flag manifolds and Stein extensions of Riemannian symmetric spaces (2008)
  • Author(s): T. Matsuki
  • Organizer: 日露ワークショップ
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2008-02-19
• [Presentation] Stein extensions of symmetric spaces and the duality of orbits on flag manifolds (2007)
  • Author(s): T. Matsuki
  • Organizer: マックスプランク研究所セミナー
  • Place of Presentation: マックスプランク数学研究所
  • Year and Date: 2007-07-02
• [Remarks]
  • URL: http://www.math.h.kyoto-u.ac.jp/~matsuki
• [Remarks]
  • URL: http://www.math.h.kyoto-u.ac.jp/~matsuki
• [Remarks]
  • URL: http://www.math.h.kyoto-u.ac.jp/~matsuki
• [Remarks]
  • URL: http://www.math.h.kyoto-u.ac.jp/~matsuki/