modules for a vertex subalgebra

• Project/Area Number: 15K04770
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: tanabe kenichiro 北海道大学, 理学研究院, 准教授 (10334038)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 頂点代数 / 代数学

Outline of Final Research Achievements

I have studied weak modules for a vertex (operator) algebra. I classified the irreducible weak modules with a Whittaker vector for the fixed point subalgebra of the Heisenberg vertex algebra under the action of an automorphism of order 2. I also obtained similar results for singlet vertex algebras

Research Products

• [Journal Article] Simple weak modules for the fixed point subalgebra of the Heisenberg vertex operator algebra of rank 1 by an automorphism of order 2 and Whittaker vectors (2017)
  • Author(s): K. Tanabe
  • Journal Title: Proceedings of the American Mathematical Society Volume: 145 Issue: 10 Pages: 4127-4140
  • DOI: 10.1090/proc/13767
  • Peer Reviewed
• [Journal Article] A generalization of intertwining operators for vertex operator algebras (2017)
  • Author(s): K. Tanabe
  • Journal Title: J. Algebra Volume: 491 Pages: 372-401
  • DOI: 10.1016/j.jalgebra.2017.08.011
  • Peer Reviewed
• [Journal Article] A generalization of twisted modules over vertex algebras (2015)
  • Author(s): Kenichiro Tanabe
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 67 Issue: 3 Pages: 1109-1146
  • DOI: 10.2969/jmsj/06731109
  • NAID: 130005094195
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] ランク1 の負定値偶格子に付随する頂点代数の不変部分代数の既約弱加群について (2018)
  • Author(s): 田邊顕一朗
  • Organizer: FINITE GROUPS, VOAS, AND RELATED TOPICS 2018
• [Presentation] Simple weak modules for some subalgebras of the Heisenberg vertex algebra and Whittaker vectors (2017)
  • Author(s): Kenichiro Tanabe
  • Organizer: VOA and related topics
  • Place of Presentation: 大阪大学大学院情報科学研究科 (大阪府・吹田市)
  • Year and Date: 2017-03-15
  • Int'l Joint Research
• [Presentation] Simple weak modules for some vertex operator algebras and Whittaker vectors (2017)
  • Author(s): Kenichiro Tanabe
  • Organizer: Finite Groups and Vertex Operator Algebras 2017
  • Place of Presentation: 東京女子大学 (東京都杉並区)
  • Int'l Joint Research
• [Presentation] 頂点代数の表現と結合的代数 (2016)
  • Author(s): 田辺 顕一朗
  • Organizer: 第61回 代数学シンポジウム
  • Place of Presentation: 佐賀大学本庄キャンパス(佐賀県・佐賀市)
  • Year and Date: 2016-09-07
  • Invited
• [Presentation] A generalization of intertwining operators for vertex operator algebras (2016)
  • Author(s): Kenichiro Tanabe
  • Organizer: Workshop on Finite Groups, VOA, and algebraic combinatorics
  • Place of Presentation: 礁溪 (台湾)
  • Year and Date: 2016-03-22
  • Int'l Joint Research
• [Presentation] A generalization of intertwining operators for vertex algebras (2015)
  • Author(s): Kenichiro Tanabe
  • Organizer: Vertex Operator Algebra and Related Topics
  • Place of Presentation: 成都 (中国)
  • Year and Date: 2015-09-08
  • Int'l Joint Research
• [Presentation] 頂点代数のintertwining operatorの一般化について (2015)
  • Author(s): 田辺顕一朗
  • Organizer: 第３２回代数的組合せ論シンポジウム
  • Place of Presentation: 金沢大学サテライト・プラザ (石川県金沢市)
  • Year and Date: 2015-06-24