Fusion rules for irrational vertex operator algebras

• Project/Area Number: 23740019
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: University of Tsukuba (2012); Osaka University (2011)
• Principal Investigator: ARIKE Yusuke 筑波大学, 数理物質系, 助教 (50583770)
• Project Period (FY): 2011 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 頂点作用素代数 / 共形場理論 / フュージョン則

Research Abstract

We determine the dimensions of the spaces of intertwining operators among irreducible modules for the vertex operator algebra arising from symplectic fermions. We also determine the dimensions of the spaces of logarithmic intertwining operators among indecomposable modules for the vertex operator superalgebra arising from symplectic fermions. By using this result we calculated tensor products of some indecomposable modules.

Research Products

• [Journal Article] Intertwining operators and fusion rules for vertex operator algebras arising from symplectic fermions (2013)
  • Author(s): Toshiyuki Abe, Yusuke Arike
  • Journal Title: Journal of Algebra Volume: 373 Pages: 39-64
  • Peer Reviewed
• [Presentation] Pseudo-trace functions on twisted modules (2013)
  • Author(s): Yusuke Arike
  • Organizer: Taitung workshop on group theory, VOA, and algebraic combinatorics
  • Place of Presentation: National Taitung University (台湾)
  • Year and Date: 2013-03-28
• [Presentation] ホップ代数と量子群-応用の可能性 (2012)
  • Author(s): 有家雄介
  • Organizer: Logarithmic intertwining operators for the symplectic fermionic vertex operator superalgebras
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2012-09-02
• [Presentation] Fusion products for the symplectic fermionic vertex operator superalgebras (2012)
  • Author(s): Yusuke Arike
  • Organizer: Conference on Vertex Operator Algebras and Related Topics
  • Place of Presentation: Shanghai Jiao Tong University (中華人民共和国)
  • Year and Date: 2012-08-26
• [Presentation] Fusion rules for vertex operator algebras arising from symplectic fermions (2012)
  • Author(s): 有家雄介
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京理科大学
• [Presentation] Fusion products for the symplectic fermionic vertex operator superalgebra
  • Author(s): 有家雄介
  • Organizer: Conference on Vertex Operator Algebras and Related Topics
  • Place of Presentation: Shanghai Jiao Tong University (中華人民共和国)
  • Invited
• [Presentation] Logarithmic intertwining operators for the symplectic fermionic vertex operator superalgebra
  • Author(s): 有家雄介
  • Organizer: ホップ代数と量子群―応用の可能性
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] Pseudo-trace functions on twisted modules
  • Author(s): 有家雄介
  • Organizer: Taitung workshop on group theory, VOA and algebraic combinatorics
  • Place of Presentation: National Taitung University (台湾)
  • Invited