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Study on the representation theory of affine Lie superalgebras and its applications

Research Project

Project/Area Number 24540014
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionUniversity of Fukui

Principal Investigator

Koga Yoshiyuki  福井大学, 学術研究院工学系部門, 准教授 (20338429)

Project Period (FY) 2012-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords超リー代数 / ワイル亜群
Outline of Final Research Achievements

In this research, we obtain the following results on highest weight representations over the affine Lie superalgebra of type sl(2,1): We study the structure of the Jantzen filtration of certain generalized Verma modules. As an application, we construct the BGG type resolutions of irreducible highest weight representations. Moreover, in order to describe the structure of generalized Verma modules by using the Weyl groupoid, we reveal a relation between the Weyl groupoids introduced by Heckenberger-Yamane and Sergeev-Veselov.

Report

(6 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (5 results)

All 2017 2015 2014 2012

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (4 results)

  • [Journal Article] Enright functors for Kac-Moody superalgebras2012

    • Author(s)
      K. Iohara, Y. Koga
    • Journal Title

      Abh. Math. Semin. Univ. Hambg.

      Volume: 82 Issue: 2 Pages: 205-226

    • DOI

      10.1007/s12188-012-0071-x

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] BGG type resolutions for the affine Lie superalgebra sl (2 ; 1)^2017

    • Author(s)
      古閑義之
    • Organizer
      Workshop VOA and related topics
    • Place of Presentation
      大阪大学大学院情報科学研究科
    • Year and Date
      2017-03-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] アフィン超リー代数 sl(2,1)^ のある一般化されたVerma 加群の構造2017

    • Author(s)
      古閑義之
    • Organizer
      Meeting for Study of Number theory, Hopf algebras and related topics
    • Place of Presentation
      富山大学理学部
    • Year and Date
      2017-02-13
    • Related Report
      2016 Annual Research Report
  • [Presentation] On admissible representations of affine Lie superalgebra sl(2,1)^2015

    • Author(s)
      古閑義之
    • Organizer
      Meeting of Hopf, quantum and super algebras
    • Place of Presentation
      富山大学大学院理工学研究部
    • Year and Date
      2015-09-18
    • Related Report
      2015 Research-status Report
  • [Presentation] アフィン超リー代数sl(2; 1)^ のBGG 型resolution について2014

    • Author(s)
      古閑義之
    • Organizer
      代数群と量子群の表現論研究会
    • Place of Presentation
      富山勤労総合福祉センター呉羽ハイツ
    • Year and Date
      2014-06-03
    • Related Report
      2014 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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