Geometric methods in vertex algebras

• Project/Area Number: 26610006
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Arakawa Tomoyuki 京都大学, 数理解析研究所, 准教授 (40377974)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2016: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2015: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2014: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
• Keywords: 群の表現 / 頂点作用素代数 / 群論(含群の表現論） / 随伴多様体 / 冪零軌道 / 群論 / 表現論

Outline of Final Research Achievements

We introduced the notion of the asymptotic algebra of the chiral differential operators and realized the simple affine W-algebras at the critical level as the global section of the asymptotic algebra of the chiral differential operators on the jet scheme of Slodowy varieties (joint work with T. Kuwabara and F. Malikov). Also, we studied the modular representation theory of affine Kac-Moody algebras via Wakimoto modules (joint work with W. Wang).

Research Products

• [Int'l Joint Research] University of Virginia/University of Denver(米国)
• [Int'l Joint Research] The University of Manchester(英国)
• [Int'l Joint Research] the University of Poitiers(フランス)
• [Int'l Joint Research] Universidade de Sao Paulo/Universidade Federal do ABC/Universidade Federal Fluminense(ブラジル)
• [Int'l Joint Research] Academia Sinica(台湾)
• [Int'l Joint Research]
• [Int'l Joint Research] University of Southern California/University of Virginia/UNIVERSITY OF DENVER(米国)
• [Int'l Joint Research] University of Poitiers(France)
• [Int'l Joint Research] University of Alberta(Canada)
• [Int'l Joint Research] Academia Sinica(Taiwan)
• [Int'l Joint Research] Sao Paulo University(Brazil)
• [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) Issue: 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
  • ISBN: 9789811026355, 9789811026362
  • Peer Reviewed / 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 Issue: 2 Pages: 397-417
  • DOI: 10.1017/s1474748016000025
  • Peer Reviewed / Int'l Joint Research / 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 Issue: 3 Pages: 1151-1178
  • DOI: 10.1007/s00220-017-2872-3
  • 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
  • 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] Rationality of admissible affine vertex algebras in the category O (2016)
  • Author(s): Tomoyuki Arakawa
  • Journal Title: Duke Math. J, Volume: 165 Issue: 1 Pages: 67-93
  • DOI: 10.1215/00127094-3165113
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Associated varieties of modules over Kac-Moody algebras and C2-cofiniteness of W-algebras (2015)
  • Author(s): Tomoyuki Arakawa
  • Journal Title: Int. Math. Res. Notices Volume: 264
  • DOI: 10.1093/imrn/rnu277
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Localization of affine W-algebras (2015)
  • Author(s): Tomoyuki Arakawa, Toshiro Kuwabara, Fedor Malikov
  • Journal Title: Comm. Math. Phys. Volume: 335 Issue: 1 Pages: 143-182
  • DOI: 10.1007/s00220-014-2183-x
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Rationality of W-algebras: principal nilpotent cases (2015)
  • Author(s): Tomoyuki Arakawa
  • Journal Title: Ann. Math. Volume: 182 Pages: 565-604
  • DOI: 10.4007/annals.2015.182.2.4
  • NAID: 120005676633
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Zhu's algebra, C2 -algebra and C2 -cofiniteness of parafermion vertex operator algebras (2014)
  • Author(s): Tomoyuki Arakawa, Ching Hung Lam, and Hiromichi Yamada
  • Journal Title: Advances in Mathematics Volume: 264 Pages: 261-295
  • DOI: 10.1016/j.aim.2014.07.021
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Two-sided BGG resolutions of admissible representations (2014)
  • Author(s): Tomoyuki Arakawa
  • Journal Title: Representation Theory Volume: 18 Issue: 7 Pages: 183-222
  • DOI: 10.1090/s1088-4165-2014-00454-0
  • NAID: 120005537655
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Deligne exceptional series, Feigin-Frenkel conjecture, and W-algebras (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Boston University Geometry and Physics Seminar
  • Place of Presentation: Boston University, USA.
  • Year and Date: 2016-03-16
  • Int'l Joint Research / Invited
• [Presentation] Associated varieties of vertex algebras (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: MIT Infinite Dimensional Algebra Seminar
  • Place of Presentation: MIT, USA
  • Year and Date: 2016-02-05
  • 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
  • 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, USA
  • Int'l Joint Research / Invited
• [Presentation] Vertex algebras and symplectic varieties (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Algebra Seminar
  • Place of Presentation: University of Zagreb, Croatia
  • 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
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Beyond C2-cofinitneness (2016)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Seminar on Algebra
  • Place of Presentation: University of Zagreb, Croatia
  • Int'l Joint Research / Invited
• [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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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, Australia
  • Int'l Joint Research / Invited
• [Presentation] Modular invariance of trace functions of Kac-Wakimoto admissible representations (2015)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Lie and Jordan algebras, Their representations and Applications VI, dedicated to Efin Zelmanov’s 60th birthday
  • Place of Presentation: Bento Goncalves, Brazil
  • Year and Date: 2015-12-13
  • Int'l Joint Research / Invited
• [Presentation] Joseph ideals and lisse minimal W-algebras (2015)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Algebra Seminar
  • Place of Presentation: Universidade Federal Fluminense, Rio de Janeiro, Brazil
  • Year and Date: 2015-12-04
  • Int'l Joint Research / Invited
• [Presentation] Associated varieties of vertex algebras (2015)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Algebra Seminar
  • Place of Presentation: Universidade de S ̃ao Paulo, Sao Paulo, Brazil.
  • Year and Date: 2015-11-19
  • Int'l Joint Research / Invited
• [Presentation] Sheets and affine vertex algebras (2015)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Vertex operator algebra and Related Topics
  • Place of Presentation: Sichuan University, Chengdu, China
  • Year and Date: 2015-09-10
  • Int'l Joint Research / Invited
• [Presentation] Joseph ideals and lisse minimal W-algebras (2015)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Summer School and Workshop on Lie Theory and Representation Theory IV
  • Place of Presentation: East China Normal University, Shanghai, China
  • Year and Date: 2015-07-02
  • Int'l Joint Research / Invited
• [Presentation] Nilpotent orbits and minimal models of W-algebras (2015)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Aspects of Lie Theory
  • Place of Presentation: INdAM 2015, Rome, Italy,
  • Year and Date: 2015-01-07 – 2015-01-10
  • Invited
• [Presentation] Introduction to W-algebras and their representation theory (Mini-course) (2014)
  • Author(s): Tomoyuki Arakawa
  • Organizer: INdAM Intensive Period - FIRB Project “Perspectives in Lie Theory”
  • Place of Presentation: The Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy
  • Year and Date: 2014-12-08 – 2014-12-24
  • Invited
• [Presentation] Localization of affine W-algebras at the critical level (2014)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Algebra Seminar
  • Place of Presentation: Technische Universit Darmstadt, Darmstadt, Germany
  • Year and Date: 2014-10-21
  • Invited
• [Presentation] Nilpotent orbits, affine Kac-Moody algebras, and affine W-algebra (2014)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Seminaire Caen Cergy Clermont Paris - Theorie des Representations
  • Place of Presentation: Universit Paris Diderot-Paris 7, Paris, France
  • Year and Date: 2014-10-17
  • Invited
• [Presentation] Orbites nilpotentes et W-algebres affines (2014)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Seminaire d'algebra;bre de Lyon
  • Place of Presentation: Lyon, France
  • Year and Date: 2014-10-09
  • Invited
• [Presentation] Nilpotent orbits and affine W-algebras (2014)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Seminaire "Groupes de Lie et espaces des modules”
  • Place of Presentation: Universit de Geneve, Geneve, Switzerland
  • Year and Date: 2014-10-07
  • Invited
• [Presentation] Localization of affine W-algebras at the critical level (2014)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Algebra Seminar
  • Place of Presentation: Universit de Poitiers, France
  • Year and Date: 2014-10-02
  • Invited
• [Presentation] 冪零軌道とW代数 (2014)
  • Author(s): 荒川 知幸
  • Organizer: 第59回代数学シンポジウム
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2014-09-08 – 2014-09-11
  • Invited
• [Presentation] Minimal models of W-algebras (2014)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Algebraic Lie theory and representation theory
  • Place of Presentation: The International Centre for Mathematical Sciences (ICMS), Edinburgh, UK.
  • Year and Date: 2014-09-01 – 2014-09-05
  • Invited
• [Presentation] Feigin-Frenkel, Adamovic-Milas, and Frenkel-Kac-Wakimoto (2014)
  • Author(s): Tomoyuki Arakawa
  • Organizer: Workshop “Lie theory and mathematical physics"
  • Place of Presentation: Centre de recherches mathematiques, Universite de Montreal, Canada
  • Year and Date: 2014-05-19 – 2014-05-23
  • Invited
• [Remarks] 荒川 知幸
  • URL: http://www.kurims.kyoto-u.ac.jp/~arakawa/