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

• Project/Area Number: 24540014
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: University 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: ¥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.

Research Products

• [Journal Article] Enright functors for Kac-Moody superalgebras (2012)
  • 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
  • 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
• [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
• [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
• [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