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Research on vertex operator algebras associated with parafermion algebras

Research Project

Project/Area Number 23540009
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionHitotsubashi University

Principal Investigator

YAMADA Hiromichi  一橋大学, 大学院経済学研究科, 教授 (50134888)

Research Collaborator ARAKAWA Tomoyuki  京都大学, 数理解析研究所, 准教授 (40377974)
TANABE Kenichiro  北海道大学, 大学院・理学研究院, 准教授 (10334038)
CHING Hung Lam  Academia Sinica(台湾), 教授
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords頂点作用素代数 / パラフェルミオン代数 / アフィンリー代数 / W代数 / 国際研究者交流 / 台湾 / 中国 / アメリカ / ブルガリア
Research Abstract

We study parafermion vertex operator algebras, which are subalgebras of integrable representations of affine Lie algebras of type A1. Using singular vectors, we classify the irreducible modules for the parafermion vertex operator algebras. Furthermore, C2-cofiniteness is established. It is proved that the dimension of Zhu's algebra coincides with that of C2 algebra. The orbifold of a lattice vertex operator algebra associated with a square root 2 times an ordinary root lattice of type An by an automorphism of order 3 is studied. We classify the irreducible modules for the orbifold. The rationality and C2-cofiniteness of the orbifold are also established.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (33 results)

All 2014 2013 2012 2011 Other

All Journal Article (3 results) (of which Peer Reviewed: 1 results) Presentation (27 results) (of which Invited: 7 results) Book (1 results) Remarks (2 results)

  • [Journal Article] Fixed point subalgebras of lattice vertex operator algebras by an automorphism of order three2013

    • Author(s)
      K. Tanabe, H. Yamada
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 65 Issue: 4 Pages: 1169-1242

    • DOI

      10.2969/jmsj/06541169

    • NAID

      130003384669

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Singular vectors and Zhu's Poisson algebra of parafermion vertex operator algebras2013

    • Author(s)
      T. Arakawa, C.H. Lam, H. Yamada
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: Vol.36 Pages: 391-398

    • DOI

      10.1007/978-4-431-54270-4_27

    • ISBN
      9784431542698, 9784431542704
    • Related Report
      2013 Final Research Report
  • [Journal Article] Singular vectors and Zhu's Poisson algebra of parafermion vertex operator algebras2013

    • Author(s)
      Tomoyuki Arakawa, Ching Hung Lam, Hiromichi Yamada
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 36 Pages: 391-398

    • Related Report
      2013 Annual Research Report
  • [Presentation] Z_k-codes and vertex operator algebras, Hualien Workshop on Finite Groups2014

    • Author(s)
      山田裕理
    • Organizer
      VOA, Algebraic Combinatorics and related topics
    • Place of Presentation
      National Dong Hua University, 台湾
    • Year and Date
      2014-03-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Vertex operator algebras associated with Zk-codes2014

    • Author(s)
      山田裕理
    • Organizer
      RIMS研究集会「有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所, 京都市
    • Year and Date
      2014-03-05
    • Related Report
      2013 Final Research Report
  • [Presentation] characterization of parafermion vertex operator algebras, RIMS Camp-Style Seminar2013

    • Author(s)
      山田裕理
    • Organizer
      Beyond the Moonshine
    • Place of Presentation
      ホテル華乃湯, 仙台市
    • Year and Date
      2013-07-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Virasoro vectors of certain orbifolds2013

    • Author(s)
      山田裕理
    • Organizer
      Taitung Workshop
    • Place of Presentation
      National Taitung University, 台湾
    • Year and Date
      2013-03-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Conformal vectors in a certain orbifold2013

    • Author(s)
      山田裕理
    • Organizer
      RIMS研究集会「有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所, 京都市
    • Year and Date
      2013-01-07
    • Related Report
      2013 Final Research Report
  • [Presentation] パラフェルミオン頂点作用素代数のZhu代数とC_2代数2012

    • Author(s)
      山田裕理
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学, 福岡市
    • Year and Date
      2012-09-19
    • Related Report
      2013 Final Research Report
  • [Presentation] C_2-cofiniteness of parafermion vertex operator algebras, Conference on Groups2012

    • Author(s)
      山田裕理
    • Organizer
      VOAs and related Structures in Honor of Masahiko Miyamoto
    • Place of Presentation
      筑波大学, つくば市
    • Year and Date
      2012-09-14
    • Related Report
      2013 Final Research Report
  • [Presentation] A characterization of parafermion vertex operator algebras2012

    • Author(s)
      山田裕理
    • Organizer
      Seminar at Sichuan University
    • Place of Presentation
      Chengdu, 中国
    • Year and Date
      2012-09-01
    • Related Report
      2013 Final Research Report
  • [Presentation] Commutant and parafermion vertex operator algebras2012

    • Author(s)
      山田裕理
    • Organizer
      Conference on Vertex Operator Algebras and Related Topics
    • Place of Presentation
      Shanghai Jiao Tong University, Shanghai, 中国
    • Year and Date
      2012-08-26
    • Related Report
      2013 Final Research Report
  • [Presentation] パラフェルミオン頂点作用素代数のC_2有限性2012

    • Author(s)
      山田裕理
    • Organizer
      RIMS研究集会「有限群とその表現, 頂点作用素代数, 組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所, 京都市
    • Year and Date
      2012-03-06
    • Related Report
      2013 Final Research Report
  • [Presentation] On parafermion vertex operator algebras2012

    • Author(s)
      山田裕理
    • Organizer
      研究集会「有限群と頂点作用素代数」
    • Place of Presentation
      東京女子大学, 杉並区
    • Year and Date
      2012-02-17
    • Related Report
      2013 Final Research Report
  • [Presentation] パラフェルミオン頂点作用素代数のC2有限性2012

    • Author(s)
      山田 裕理
    • Organizer
      RIMS研究集会「有限群とその表現、頂点作用素代数、組合せ論の研究」(招待講演)
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Research-status Report
  • [Presentation] On parafermion vertex operator algebras2012

    • Author(s)
      山田 裕理
    • Organizer
      研究集会「有限群と頂点作用素代数」(招待講演)
    • Place of Presentation
      東京女子大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Zhu's C_2-algebra of parafermion vertex operator algebras2011

    • Author(s)
      山田裕理
    • Organizer
      Zhu's C2-algebra of parafermion vertex operator algebras
    • Place of Presentation
      Academia Sinica, 台湾
    • Year and Date
      2011-12-22
    • Related Report
      2013 Final Research Report
  • [Presentation] パラフェルミオン頂点作用素代数のC_2代数2011

    • Author(s)
      山田裕理
    • Organizer
      第9回「代数学と計算」研究集会
    • Place of Presentation
      首都大学東京, 八王子市
    • Year and Date
      2011-11-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Singular vectors and Zhu's Poisson algebra of parafermion vertex operator algebras, International Workshop2011

    • Author(s)
      山田裕理
    • Organizer
      Lie Theory and Its Applications in Physics
    • Place of Presentation
      Bulgarian Academy of Sciences, Varna, Bulgaria
    • Year and Date
      2011-06-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Zhu's C2-algebra of parafermion vertex operator algebras2011

    • Author(s)
      山田 裕理
    • Organizer
      Conference on Vertex Operator Algebras, Finite Groups and Related Topics(招待講演)
    • Place of Presentation
      台湾中央研究院
    • Related Report
      2011 Research-status Report
  • [Presentation] パラフェルミオン頂点作用素代数のC2代数2011

    • Author(s)
      山田 裕理
    • Organizer
      第9回「代数学と計算」研究集会
    • Place of Presentation
      首都大学東京
    • Related Report
      2011 Research-status Report
  • [Presentation] Singular vectors and Zhu's Poisson algebra of parafermion vertex operator algebras2011

    • Author(s)
      山田 裕理
    • Organizer
      International Workshop「Lie Theory and Its Applications in Physics」(招待講演)
    • Place of Presentation
      ブルガリア科学アカデミー
    • Related Report
      2011 Research-status Report
  • [Presentation] Z_k-codes and vertex operator algebras

    • Author(s)
      山田 裕理
    • Organizer
      Hualien Workshop on Finite Groups
    • Place of Presentation
      National Dong Hua University, Taiwan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Vertex operator algebras associated with Z_k-codes

    • Author(s)
      山田 裕理
    • Organizer
      RIMS研究集会 「有限群とその表現、頂点作用素代数、代数的組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A characterization of parafermion vertex operator algebras

    • Author(s)
      山田 裕理
    • Organizer
      RIMS Camp-Style Seminar 「Beyond the Moonshine」
    • Place of Presentation
      ホテル華乃湯(仙台市)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Virasoro vectors of certain orbifolds

    • Author(s)
      山田 裕理
    • Organizer
      Taitung Workshop
    • Place of Presentation
      National Taitung University, 台湾
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Conformal vectors in a certain orbifold

    • Author(s)
      山田 裕理
    • Organizer
      RIMS研究集会「有限群とその表現、頂点作用素代数、代数的組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] パラフェルミオン頂点作用素代数の Zhu 代数と C2 代数

    • Author(s)
      山田 裕理
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] C2-cofiniteness of parafermion vertex operator algebras

    • Author(s)
      山田 裕理
    • Organizer
      Conference on Groups, VOAs and related Structures
    • Place of Presentation
      筑波大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Commutant and parafermion vertex operator algebras

    • Author(s)
      山田 裕理
    • Organizer
      Conference on Vertex Operator Algebras and Related Topics
    • Place of Presentation
      Shanghai Jiao Tong University, 中国
    • Related Report
      2012 Research-status Report
    • Invited
  • [Book] Lie Theory and Its Applications in Physics2013

    • Author(s)
      Vladimir Dobrev
    • Total Pages
      554
    • Publisher
      Springer
    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      https://hri.ad.hit-u.ac.jp/html/181_research_activity_ja.html

    • Related Report
      2013 Final Research Report
  • [Remarks] 一橋大学研究者情報

    • URL

      https://hri.ad.hit-u.ac.jp/html/181_research_activity_ja.html

    • Related Report
      2013 Annual Research Report

URL: 

Published: 2011-08-05   Modified: 2023-03-16  

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