Ｗ代数の表現論の新展開

2016 Fiscal Year Annual Research Report

• Project/Area Number: 25287004
• Research Institution: Kyoto University
• Principal Investigator: 荒川 知幸 京都大学, 数理解析研究所, 准教授 (40377974)
• Co-Investigator(Kenkyū-buntansha): 山内 博 東京女子大学, 公私立大学の部局等, 准教授 (40452213) ; 山田 裕理 一橋大学, 経済学研究科(研究院), その他 (50134888) ; 和田 堅太郎 信州大学, 理学部, 准教授 (60583862)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 群論（含群の表現論） / 頂点作用素代数

Outline of Annual Research Achievements

昨年度までに得られた本研究課題の成果をいくつかの国際研究集会、談話会、セミナーなどで報告した。主なものとしては以下が挙げらえる。(1)オーストラリア数学会60周年記念年会での基調講演(2)MITでの半年間の大学院生向けの特別講義(3)７件の国外談話会講演(4)プレミータ研究所(カナダ)の物理学の研究集会での連続招待講演。

研究面では、2014年度にピサ（イタリア）のCRM研究所で行った集中講義をもとに、これまでの結果を講義録として整理した(Springerから出版予定)。その他に(1)アフィンリー環の許容表現に付随する共型場理論に関して、V. FutornyとL.-E.Ramirezと共同研究でウエイト加群の分類の研究を行った(オンライン出版済み).(2) 研究分担者の山田裕理と山内博と共同研究で、Z/nZコードに付随する頂点代数を研究した(出版済).(3) T. Creutzig, 川節和哉, A. Linshawと共同研究で極小W代数のオービフォールドとコセットを研究した(CMPから出版予定). (4) A. Premetと共同研究で, アフィンW代数を使って中心化部分代数に付随するMishchenko-Fomenko代数の量子化が可能なことを示した(Proceedings of Moscow Math. Society のVinberg８０歳記念号から出版予定).(5) J. van Ekerenと共同研究で, アフィンリー環の許容表現の一般一点関数のモジュラー不変性を証明した(プレプリント).(6) C.-H. Lamと山田裕理と共同研究でパラフェルミオン頂点代数とW代数の関係を明らかにした（投稿中).(7) C. Jiangと共同研究で, 主W代数のコセット実現をsl_3の場合に証明した（投稿中).

Research Progress Status

28年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

28年度が最終年度であるため、記入しない。

Causes of Carryover

28年度が最終年度であるため、記入しない。

Expenditure Plan for Carryover Budget

28年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] the University of Virginia/University of Denver(米国)
  • Country Name: U.S.A.
  • Counterpart Institution: the University of Virginia/University of Denver
• [Int'l Joint Research] University of Poitiers(フランス)
  • Country Name: FRANCE
  • Counterpart Institution: University of Poitiers
• [Int'l Joint Research] The University of Manchester(英国)
  • Country Name: UNITED KINGDOM
  • Counterpart Institution: The University of Manchester
• [Int'l Joint Research] The University of Sydney(オーストラリア)
  • Country Name: AUSTRALIA
  • Counterpart Institution: The University of Sydney
• [Int'l Joint Research] Universidade de Sao Paulo/Universidade Federal Fluminense(ブラジル)
  • Country Name: BRAZIL
  • Counterpart Institution: Universidade de Sao Paulo/Universidade Federal Fluminense
• [Int'l Joint Research]
  • # of Other Countries: 2
• [Journal Article] Explicit generators in rectangular affine W-algebras of type A (2017)
  • Author(s): Tomoyuki Arakawa and Alexander Molev
  • Journal Title: Lett. Math. Phys. Volume: 107(1) Pages: 47-59
  • DOI: 10.1007/s11005-016-0890-2
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Vertex operator algebras associated with Z/kZ-codes (2017)
  • Author(s): Tomoyuki Arakawa, Hiromichi Yamada and Hiroshi Yamauchi
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 191 Pages: 513-521
  • DOI: 10.1007/978-981-10-2636-2_38
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Weight representations of admissible affine vertex algebras (2017)
  • Author(s): Tomoyuki Arakawa, Vyacheslav Futorny and Luis Enrique Ramirez
  • Journal Title: Comm. Math. Phys. Volume: 印刷中 Pages: 印刷中
  • DOI: 10.1007/s00220-017-2872-3
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Joseph ideals and lisse minimal W-algebras (2017)
  • Author(s): Tomoyuki Arakawa and Anne Moreau
  • Journal Title: J. Inst. Math. Jussieu Volume: 印刷中 Pages: 印刷中
  • DOI: 10.1017/S1474748016000025
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Orbifolds and cosets of minimal W-algebras (2017)
  • Author(s): Tomoyuki Arakawa, Thomas Creutzig, Kazuya Kawasetsu and Andrew Linshaw
  • Journal Title: Comm. Math. Phys. Volume: 印刷中 Pages: 印刷中
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Modular affine vertex algebras and baby Wakimoto modules (2016)
  • Author(s): Tomoyuki Arakawa and Weiqiang Wang
  • Journal Title: Proc. Symp. Pure Math. Volume: 92 Pages: 14-29
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] New Realization of Cyclotomic q-Schur Algebras (2016)
  • Author(s): K. Wada
  • Journal Title: Publ. RIMS Kyoto Univ Volume: 52 Pages: 497-555
  • DOI: 10.4171/PRIMS/188
  • Peer Reviewed
• [Presentation] Parafermion VOAs and $\mathbb{Z}_k$-code VOAs (2017)
  • Author(s): 山田裕理
  • Organizer: Finite Groups and Vertex Operator Algebras 2017
  • Place of Presentation: 東京女子大学
  • Year and Date: 2017-03-21 – 2017-03-21
  • Int'l Joint Research / Invited
• [Presentation] Coset Construction of W-algebras (2017)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Algebra and Number Theory Seminar
  • Place of Presentation: UC Santa Cruz, USA
  • Year and Date: 2017-03-10 – 2017-03-10
  • Int'l Joint Research / Invited
• [Presentation] Vertex operator algebras and symplectic varieties (2017)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Colloquium
  • Place of Presentation: UC Santa Cruz, USA
  • Year and Date: 2017-03-07 – 2017-03-07
  • Int'l Joint Research / Invited
• [Presentation] GKO construction of minimal series W-algebras (2017)
  • Author(s): Tomoyuki Arakawa
  • Organizer: MIT Infinite Dimensional Algebra Seminar
  • Place of Presentation: MIT, USA
  • Year and Date: 2017-02-17 – 2017-02-17
  • Int'l Joint Research / Invited
• [Presentation] Moore-Tachikawa conjecture and chiral algebras of class S (2017)
  • Author(s): Tomoyuki Arakawa
  • Organizer: 7th Seminar on Conformal Field Theory
  • Place of Presentation: Technische Universitat Darmstadt, Germany
  • Year and Date: 2017-02-03 – 2017-02-03
  • Int'l Joint Research / Invited
• [Presentation] Moore-Tachikawa conjecture and chiral algebras of class S (2017)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Seminaire Geometrie Algebrique
  • Place of Presentation: Laboratoire Paul Painleve, Universite de Lille, France
  • Year and Date: 2017-01-31 – 2017-01-31
  • Int'l Joint Research / Invited
• [Presentation] Associated varieties of vertex algebras (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Exact operator algebras in superconformal field theories
  • Place of Presentation: Perimeter Institute for Theoretical Physics, Canada
  • Year and Date: 2016-12-14 – 2016-12-16
  • Int'l Joint Research / Invited
• [Presentation] Construction of genus zero chiral algebras of class S (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Exact operator algebras in superconformal field theories
  • Place of Presentation: Perimeter Institute for Theoretical Physics, Canada
  • Year and Date: 2016-12-14 – 2016-12-14
  • Int'l Joint Research / Invited
• [Presentation] Moore-Tachikawa conjecture and chiral algebras of class S (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: 60th Annual Meeting of the Australian Mathematical Society
  • Place of Presentation: Australian National University, Canberra,
  • Year and Date: 2016-12-05 – 2016-12-08
  • Int'l Joint Research / Invited
• [Presentation] Finite dimensional simple modules of deformed current Lie algebra (2016)
  • Author(s): K. Wada
  • Organizer: Conference on Algebraic Representation Theory,
  • Place of Presentation: Harbin Institute of Technology, Shenzhen Graduate School
  • Year and Date: 2016-12-05 – 2016-12-05
  • Int'l Joint Research / Invited
• [Presentation] Moore-Tachikawa conjecture and chiral algebras of class S (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Sydney-UNSW Joint Colloquium
  • Place of Presentation: The University of Sydney, Australia
  • Year and Date: 2016-11-25 – 2016-11-25
  • Int'l Joint Research / Invited
• [Presentation] Vertex algebras and symplectic varieties (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Colloquium
  • Place of Presentation: the University of Poitiers, France
  • Year and Date: 2016-11-02 – 2016-11-02
  • Int'l Joint Research / Invited
• [Presentation] Vertex algebras and symplectic varieties (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Colloquium
  • Place of Presentation: University of Texas at Arlington
  • Year and Date: 2016-09-30 – 2016-09-30
  • Int'l Joint Research / Invited
• [Presentation] On the 2dTQFT associated with vertex algebras (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: MIT Infinite Dimensional Algebra Seminar
  • Place of Presentation: MIT, USA
  • Year and Date: 2016-09-09 – 2016-09-09
  • Int'l Joint Research / Invited
• [Presentation] On the 2d TQFT associated with vertex algebras (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Conference in Finite Groups and Vertex Algebras dedicated to Robert L. Griess on the occasion of his 71st birthday,
  • Place of Presentation: Academia Sinica, Taipei, Taiwan
  • Year and Date: 2016-08-26 – 2016-08-26
  • Int'l Joint Research / Invited
• [Presentation] On Conway-Miyamoto correspondences for Fischer 3-transposition groups (2016)
  • Author(s): Hiroshi Yamaguchi
  • Organizer: The XXIVth International Conference on Integrable Systems and Quantum Symmetries
  • Place of Presentation: Cezch Technical University Prague (Cezch Republic)
  • Year and Date: 2016-06-17 – 2016-06-17
  • Int'l Joint Research
• [Presentation] Equivariant affine W-algebras (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Nilpotent Orbits and Representation Theory
  • Place of Presentation: Centro di Ricerca Matematica Ennio De Giorgi (CRM), Pisa, Italy
  • Year and Date: 2016-06-16 – 2016-06-16
  • Int'l Joint Research / Invited
• [Presentation] Finite dimensional simple modules of deformed current Lie algebras (2016)
  • Author(s): K. Wada
  • Organizer: 第2回Algebraic Lie Theory and Representation Theory
  • Place of Presentation: 菅平高原 プチ・ホテル ゾンタック(長野県上田市)
  • Year and Date: 2016-06-12 – 2016-06-12
• [Presentation] Beyond C2-cofinitneness (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Seminar on Algebra
  • Place of Presentation: University of Zagreb, Croatia
  • Year and Date: 2016-06-07 – 2016-06-07
  • Int'l Joint Research / Invited
• [Presentation] The Adamovic-Milas conjecture and application (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Colloquium
  • Place of Presentation: University of Zagreb, Croatia
  • Year and Date: 2016-06-01 – 2016-06-01
  • Int'l Joint Research / Invited
• [Presentation] Vertex algebras and symplectic varieties (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: CMSA Special Mathematical Physics Seminar
  • Place of Presentation: Harvard University, USA
  • Year and Date: 2016-05-13 – 2016-05-13
  • Int'l Joint Research / Invited
• [Presentation] Vertex algebras and symplectic varieties (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Algebra Seminar
  • Place of Presentation: University of Virginia
  • Year and Date: 2016-04-22 – 2016-04-22
  • Int'l Joint Research / Invited
• [Presentation] Pentagonal number theorem and representation theory (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Colloquium
  • Place of Presentation: University of Virginia
  • Year and Date: 2016-04-21 – 2016-04-21
  • Int'l Joint Research / Invited
• [Presentation] Deligne exceptional series, Feigin-Frenkel conjecture, and W-algebras (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Representation theory and symplectic singularities in honour of Sasha Premet’s 60th birthday,
  • Place of Presentation: ICMS, Edinburgh, UK
  • Year and Date: 2016-04-04 – 2016-04-04
  • Int'l Joint Research / Invited
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/~arakawa/
• [Funded Workshop] ESI conference on Geometry and Representation Theory (2017)
  • Place of Presentation: Vienna, Austria
  • Year and Date: 2017-01-16 – 2017-01-27