Construction of Conformal field theory based on Representation theory of Vertex Operator Algebra

• Project/Area Number: 22540010
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: TSUCHIYA Akihiro 東京大学, カブリ数物連携宇宙研究機構, 上級科学研究員 (90022673)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 頂点作用素代数 / 共形場理論 / Log共形場理論 / 拡大されたW代数 / 量子群 / テンソル圏 / fusion tensor積

Research Abstract

For each pair of relationaly prime positive integer p+ , p- , which are p+ , p- >2, we defined Vertex operator algebras called Extended W algebra. And we showed that (1) they satisfied Zhu’s finiteness conditions, and (2) constructed all the irreducible modules.

Research Products

• [Journal Article] On the extended W-algebra of type sl_2 at positive rational level (2013)
  • Author(s): Akihiro Tsuchiya, Simon Wood
  • Journal Title: arXiv:1302.6435 Volume: なし Pages: 59-59
• [Journal Article] The tensor structure on the representation category of the W_p triplet algebra (2012)
  • Author(s): Akihiro Tsuchiya, Simon Wood
  • Journal Title: arXiv:1201.0419 Volume: なし Pages: 56-56
• [Journal Article] The tensor structure on the representation category of the W_p triplet algebra,
  • Author(s): Akihiro Tsuchiya and Simon Wood
  • Journal Title: arXiv Volume: 1201 Pages: 419-419
• [Journal Article] On the extended W-algebra of type sl_2 at positive rational level
  • Author(s): Akihiro Tsuchiya and Simon Wood
  • Journal Title: arXiv Volume: 1302 Pages: 6435-6435
• [Presentation] Conformal Field Theory and Quantun Group (2011)
  • Author(s): Akihiro Tsuchiya
  • Organizer: 国際会議 Conformal field theories and tensor categories
  • Place of Presentation: Beijing, 中国
  • Year and Date: 2011-06-17
• [Presentation] Conformal Field Theory and Quantum Group (2011)
  • Author(s): 土屋昭博
  • Organizer: Conformal field theories and tensor categories
  • Place of Presentation: Beijing International Center、中国(招待講演)
  • Year and Date: 2011-06-17
• [Presentation] ConformalFieldTheoryandQuantunGroup (2011)
  • Author(s): 土屋昭博
  • Organizer: 日本数学会春期LowdimTopologyandNumberTheoryIII
  • Place of Presentation: 九州大学
  • Year and Date: 2011-03-16
• [Presentation] Conformal Field Theory and Quantum Group (2011)
  • Author(s): 土屋昭博
  • Organizer: Low dim Topology and Number Theory III
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2011-03-16