Study of generalized Verma modules

2011 Fiscal Year Final Research Report

• Project/Area Number: 20540011
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• 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): 2008 – 2011
• Keywords: 一般化旗多様体 / 半単純リー群 / ユニタリ表現 / 一般化バルマ加群 / 有限W代数

Research Abstract

We classified homomorphisms between scalar generalized modules associated with normal parabolic subalgebras of exceptional Lie algebras under the assumption that the infinitesimal characters are regular integral. We also studied Whittaker modules in the completion of generalized modules associated with parabolic subalgebras including Jacobi parabolic subalgebras of simple Lie algebras of the type C. We also obtained results on irreducibility of the Whittaker dual of principal series representations. We supported 49th joint Symposium on Real Analysis and Functional Analysis.

Research Products

• [Presentation] Whittaker modules and vectors associated with the Jacobi parabolic subalgebras (2011)
  • Author(s): 松本久義
  • Organizer: The 10th Workshop on Nilpotent Orbits and Representation Theory
  • Place of Presentation: 九州大学
  • Year and Date: 20110200
• [Presentation] On a finite W-algebra module structure on the space of continuous Whittaker vectors for an irreducible Harish-Chandra modules (2010)
  • Author(s): 松本久義
  • Organizer: The 9th Workshop on Nilpotent Orbits and Representation Theory
  • Place of Presentation: 北海道大学
  • Year and Date: 20100200
• [Presentation] On homomorphisms between scalar generalized Verma modules (2009)
  • Author(s): 松本久義
  • Organizer: Conference in honor of Toshio Oshima's 60th birthday Differential Equations and Symmetric Spaces
  • Place of Presentation: University of Tokyo
  • Year and Date: 20091000
• [Presentation] On existence of homomorphisms between generalized Verma modules (2009)
  • Author(s): 松本久義
  • Organizer: Representation Theory of Real Reductive Groups(国際研究集会)
  • Place of Presentation: ユタ大学
  • Year and Date: 20090700
• [Presentation] On homomorphisms between scalar generalized Verma modules (2009)
  • Author(s): 松本久義
  • Organizer: The 8th Workshop on Nilpotent Orbits and Representation Theory
  • Place of Presentation: Ogoto Shiga Japan
  • Year and Date: 20090300
• [Presentation] On homomorphisms between scalar generalized Verma modules (2008)
  • Author(s): 松本久義
  • Organizer: Mini-Workshop on Representation Theory
  • Place of Presentation: University of Tokyo
  • Year and Date: 20080900