Study on representations of conformal suepralgebras and applications to mathematical physics Study on representations of conformal suepralgebras and applications to mathematical physics

• Project/Area Number: 21740007
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: University of Fukui
• Principal Investigator: KOGA Yoshiyuki 福井大学, 大学院・工学研究科, 准教授 (20338429)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 環論(含むリー環) / アフィン超リー代数 / コンフォーマル超リー代数 / コンフォーマル超代数

Research Abstract

In this research, we obtained the following results concerning conformal superalgebras:
1. The Virasoro algebra is contained in conformal superalgebras as a subalgebra, and it plays important roles in the representation theory of conformal superalgebras. We publish a book correcting basic results in the representation theory of the Virasoro algebra in collaboration with K. Iohara (Lyon Univ.).
2. A close relation between a conformal and a Kac-Moody superalgebras is known. We study the singular vector formula for some Kac-Moody superalgebras.

Research Products

• [Journal Article] Fusion algebras for N=1 superconformal field theories through coinvariants II+1/2: Ramond sector (2009)
  • Author(s): K Iohara, Y. Koga
  • Journal Title: International Mathematics Research Notices Volume: 13 Pages: 2374-2416
  • Peer Reviewed
• [Journal Article] Note on spin modules associated to Z-graded Lie superalgebras (2009)
  • Author(s): K Iohara, Y. Koga
  • Journal Title: Journal of Mathematical physics Volume: 50 Pages: 103508-103508
  • Peer Reviewed
• [Journal Article] Fusion Algebras for N=1 Superconformal Field Theories through Coinvariants II+ 1/2 : Ramond Sector (2009)
  • Author(s): K.Iohara, Y.Koga
  • Journal Title: Int.Math.Res.Notice 13 Pages: 2374-2416
  • Peer Reviewed
• [Journal Article] Note on spin modules associated to Z-graded Lie superalgebras (2009)
  • Author(s): K.Iohara, Y.Koga
  • Journal Title: Jour.Math.Phys. 50
  • Peer Reviewed
• [Presentation] Fusion algebras for N=1 superconformal algebras: Ramond sector (2010)
  • Author(s): 古閑義之
  • Organizer: 代数群と量子群の表現論研究集会
  • Place of Presentation: すいとぴあ江南
  • Year and Date: 2010-06-04
• [Presentation] Fusion algebras for N=1 superconformal algebra : Ramond sector (2010)
  • Author(s): 古閑義之
  • Organizer: 代数群と量子群の表現論研究集会
  • Place of Presentation: すいとぴあ江南(愛知県)
  • Year and Date: 2010-06-04
• [Book] Representation Theory of the Virasoro algebra (2011)
  • Author(s): K Iohara, Y. Koga
  • Total Pages: 474
  • Publisher: Springer
• [Book] Representation Theory of the Virasoro Algebra (2011)
  • Author(s): K.Iohara, Y.Koga
  • Total Pages: 474
  • Publisher: Springer