The Radon-Penrose transforms and infinite dimensional representation theory, and their applications to the global analysis on non-compact complex homogeneous spaces

• Project/Area Number: 18540070
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: The University of Tokyo
• Principal Investigator: SEKIGUCHI Hideko The University of Tokyo, 大学院・数理科学研究科, 准教授 (50281134)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,080,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥480,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2007: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: ペンローズ変換 / 半単純リー群 / ユニタリ表現 / 有界対称領域 / 複素多様体 / 積分幾何 / 概均質ベクトル空間 / 超幾何函数

Research Abstract

Our main concern is with the characterization of the image of the Penrose transform by means of a system of partial differential equations on the cycle space. I have extended my previous results (the case that the transformation groups are indefinite unitary groups) to non-tube domains of type AIII ([1]), and also found explicit branching laws of certain singular unitary representations with respect to symmetric pairs by using the Penrose transform.

Research Products

• [Journal Article] 無限次元表現 (2010)
  • Author(s): H. Sekiguchi
  • Journal Title: 数理科学 559 Pages: 43-48
• [Journal Article] 無限次元表現 --「無限次元の魅力」 (2010)
  • Author(s): H.Sekiguchi
  • Journal Title: 数理科学(サイエンス社) 559 Pages: 43-48
• [Journal Article] 連続群とその表現論を学ぶための本 (2007)
  • Author(s): H. Sekiguchi
  • Journal Title: 応用数理 (日本応用数理学会誌) 17 Pages: 624-624
  • NAID: 110006436337
• [Journal Article] 表現論とペンローズ変換 (2006)
  • Author(s): H. Sekiguchi
  • Journal Title: 数理科学 520 Pages: 34-40
• [Journal Article] 表現論とペンローズ変換 (2006)
  • Author(s): 関口 英子
  • Journal Title: 数理科学 520 Pages: 34-40
• [Journal Article] Penrose transform for indefinite Grassmann manifolds
  • Author(s): H. Sekiguchi
  • Journal Title: accepted for publication in International Journal of Mathematics
  • Peer Reviewed
• [Journal Article] Penrose transform for indefinite Grassmann manifolds
  • Author(s): H.Sekiguchi
  • Journal Title: International Journal of Mathematics (accepted) (掲載確定)
  • Peer Reviewed
• [Presentation] Penrose transform between symmetric space (2009)
  • Author(s): H. Sekiguchi
  • Organizer: Conference in honor of Toshio Oshima' s 60th birthday "Differential Equations and symmetric Spaces"
  • Place of Presentation: The University of Tokyo, Japan
• [Presentation] Penrose transform between symmetric spaces (2009)
  • Author(s): H. Sekiguchi
  • Organizer: Conference in honor of Toshio Oshima's 60th birthday "Differential Equations and Symmetric Spaces"
  • Place of Presentation: University of Tokyo, Japan
• [Presentation] Radon-Penrose transform for the quantization of elliptic orbits (2006)
  • Author(s): H. Sekiguchi
  • Organizer: International Conference "Integral Geometry and Harmonic Analysis" (organizers : Fulton Gonzalez, Tomoyuki Kakehi, Toshio Oshima)
  • Place of Presentation: University of Tsukuba, Japan
• [Presentation] Penrose transform between symmetric spaces
  • Author(s): H. Sekiguchi
  • Organizer: Conference in honor of Toshio Oshima's 60^<th> birthday "Differential Equations and Symmetric Spaces"