Study of homomorphisms between generalized Verma modules

• Project/Area Number: 26400006
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: MATUMOTO Hisayosi 東京大学, 大学院数理科学研究科, 准教授 (50272597)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 一般化バルマ加群 / ユニタリ表現 / 半単純リー代数 / リー群 / 微分不変量 / 退化系列表現 / 放物幾何 / リー代数

Outline of Final Research Achievements

The classification problem of homomorphisms between scalar generalized Verma modules is equivalent to the classification of equivariant differential operators between line bundles over the corresponding generalized flag varieties. It plays an important role in parabolic geometry as well as representation theory. The problem remains unsolve more than 40 years. The principal investigator studied this classification problem.
The principal investigator classified homomorphisms between scalar generalized Verma modules for general linear algebras. He also gives alternative proof of a result of Borho-Jantzen, aiming to generalize it to other reductive Lie algebras.

Research Products

• [Journal Article] Homomorphisms between scalar generalized Verma modules for gl(n.C) (2016)
  • Author(s): HIsayosi MATUMOTO
  • Journal Title: International Mathematics Research Notices Volume: 2016 Issue: 12 Pages: 3525-3547
  • DOI: 10.1093/imrn/rnv238
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the homomorphisms between scalar generalized Verma modules (2014)
  • Author(s): Hisayosi MATUMOTO
  • Journal Title: Compositio MATHEMATICA Volume: 150 Issue: 5 Pages: 877-892
  • DOI: 10.1112/s0010437x13007677
  • NAID: 130008005945
  • Peer Reviewed
• [Presentation] gl(n,C) のスカラー型一般化バルマ加群の間の準同型 (2015)
  • Author(s): 松本久義
  • Organizer: Algebraic Lie Theory and Representation Theory 2015
  • Place of Presentation: 岡山いこいの村
  • Year and Date: 2015-06-08