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Study of generalized Verma modules

Research Project

Project/Area Number 20540011
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionThe 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
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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 / 一般化バルマ / 一般化Verma加群
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.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (17 results)

All 2011 2010 2009 2008

All Presentation (17 results)

  • [Presentation] Whittaker modules and vectors associated with the Jacobi parabolic subalgebras2011

    • Author(s)
      Hisayosi MATUMOTO
    • Organizer
      2011 Nankai International Workshop on Reoresentationh Theory and Harmonic Analysis
    • Place of Presentation
      Tianjin, China(招待講演)
    • Year and Date
      2011-06-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] Whittaker modules and vectors associated with the Jacobi parabolic subalgebras2011

    • Author(s)
      松本久義
    • Organizer
      The 10th Workshop on Nilpotent Orbits and Representation Theory
    • Place of Presentation
      九州大学
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] The 10th Workshop on Nilpotent Orbits and Representation Theory2011

    • Author(s)
      Whittaker modules and vectors associated with the Jacobi parabolic subalgebras
    • Place of Presentation
      九州大学
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On a finite W-algebra module structure on the space of continuous Whittaker vectors for an irreducible Harish-Chandra modules2010

    • Author(s)
      松本久義
    • Organizer
      The 9th Workshop on Nilpotent Orbits and Representation Theory
    • Place of Presentation
      北海道大学
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Presentation] The 9th Workshop on Nilpotent Orbits and Representation Theory2010

    • Author(s)
      On a finite W-algebra module structure on the space of continuous Whittaker vectors for an irreducible Harish-Chandra modules
    • Place of Presentation
      Hokkaido 北海道大学
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On homomorphisms between scalar generalized Verma modules2009

    • 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
    • Related Report
      2011 Final Research Report
  • [Presentation] On homomorphisms between scalar generalized Verma modules2009

    • Author(s)
      松本久義
    • Organizer
      The 8th Workshop on Nilpotent Orbits and Representation Theory
    • Place of Presentation
      Ogoto Shiga Japan
    • Related Report
      2011 Final Research Report
  • [Presentation] On existence of homomorphisms between generalized Verma modules2009

    • 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
    • Related Report
      2011 Final Research Report
  • [Presentation] Representation Theory of Real Reductive Groups2009

    • Author(s)
      On exisitence of homomorphisms between generfalized Verma modules
    • Place of Presentation
      ユタ大学
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] The 8th Workshop on Nilpotent Orbits and Representation Theory2009

    • Author(s)
      On homomorphisms between scalar generalized Verma modules
    • Place of Presentation
      雄琴
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Conference in honor of Toshio Oshima's 60th birthday "Differential Equations and Symmetric Spaces2009

    • Author(s)
      On homomorphisms between scalar generalized Verma modules
    • Place of Presentation
      東京大学
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On exisitence of homomorphisms between generfalized Verma modules2009

    • 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
    • Related Report
      2009 Annual Research Report
  • [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 Equtions and Symmetric Spaces
    • Place of Presentation
      Univercsity of Tokyo
    • Related Report
      2008 Annual Research Report
  • [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
    • Related Report
      2008 Annual Research Report
  • [Presentation] On homomorphisms between scalar generalized Verma modules2008

    • Author(s)
      松本久義
    • Organizer
      Mini-Workshop on Representation Theory
    • Place of Presentation
      University of Tokyo
    • Related Report
      2011 Final Research Report
  • [Presentation] Mini-Workshop on Representation Theory2008

    • Author(s)
      On homomorphisms between scalar generalized Verma modules
    • Place of Presentation
      東京大学
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On homomorphisms between scalar generalized Verma modules,2008

    • Author(s)
      松本久義
    • Organizer
      Mini-Workshop on Representation Theory
    • Place of Presentation
      Univercsity of Tokyo
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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