Orbit decomposition of multiple flag varieties

• Project/Area Number: 22540016
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Ryukoku University
• Principal Investigator: MATSUKI Toshihiko 龍谷大学, 文学部, 教授 (20157283)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 代数群 / リー群 / リー環 / 表現論

Research Abstract

We described orbits on a typical triple flag variety of orthogonal group of odd degree. This result holds over an arbitrary field of characteristic not two. As byproducts, we obtained orbit decompositions of the flag variety for the general linear group by various subgroups. We also computed number of orbits and number of elements in each orbits when the field is finite.

Research Products

• [Journal Article] An example of orthogonal triple flag variety of finite type, J. of Algebra (2013)
  • Author(s): Toshihiko Matsuki
  • Journal Title: J. of Algebra Volume: 375 Pages: 148-187
  • DOI: 10.1016/j.jalgebra.2012.11.012
  • Peer Reviewed
• [Presentation] 有限個の軌道を持つ直交型三重旗多様体の例 (2011)
  • Author(s): 松木敏彦
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-10-01
• [Presentation] 直交型三重旗多様体の軌道分解の一例 (2011)
  • Author(s): 松木敏彦
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-10-01
• [Presentation] 直交型三重旗多様体の軌道分解の一例 (2011)
  • Author(s): 松木敏彦
  • Organizer: 数理解析研究所研究集会(表現論と調和解析における諸問題)
  • Place of Presentation: 京都大学
  • Year and Date: 2011-06-30
• [Remarks]
  • URL: http://www.ab.auone-net.jp/~matsuki/
• [Remarks] Home page of Toshihiko MATSUKI (松木敏彦)
  • URL: http://www.ab.auone-net.jp/~matsuki/
• [Remarks]
  • URL: http://www.ab.auone-net.jp/~matsuki/
• [Remarks]
  • URL: http://www.ab.auone-net.jp/~matsuki/