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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Parafermion vertex operator algebras and $ W$-algebras


Authors: Tomoyuki Arakawa, Ching Hung Lam and Hiromichi Yamada
Journal: Trans. Amer. Math. Soc. 371 (2019), 4277-4301
MSC (2010): Primary 17B69; Secondary 17B65
DOI: https://doi.org/10.1090/tran/7547
Published electronically: October 23, 2018
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Abstract: We prove the conjectural isomorphism between the level $ k$ $ \widehat {\mathfrak{sl}}_2$-parafermion vertex operator algebra and the $ (k+1,k+2)$-minimal series $ W_k$-algebra for all $ k \ge 2$. As a consequence, we obtain the conjectural isomorphism between the $ (k+1,k+2)$-minimal series $ W_k$-algebra and the coset vertex operator algebra $ SU(k)_1\otimes SU(k)_1/SU(k)_2$.


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Additional Information

Tomoyuki Arakawa
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: arakawa@kurims.kyoto-u.ac.jp

Ching Hung Lam
Affiliation: Institute of Mathematics, Academia Sinica, Taipei 115, Taiwan
Email: chlam@math.sinica.edu.tw

Hiromichi Yamada
Affiliation: Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan
Email: yamada.h@r.hit-u.ac.jp

DOI: https://doi.org/10.1090/tran/7547
Received by editor(s): February 14, 2017
Received by editor(s) in revised form: January 12, 2018
Published electronically: October 23, 2018
Additional Notes: The first author was partially supported by JSPS KAKENHI Grants No. 17H01086 and No. 17K18724, the second author was partially supported by MoST Grant No. 104-2115-M-001-004-MY3 of Taiwan, and the third author was partially supported by JSPS Grant-in-Aid for Scientific Research No. 26400040. Part of the work was done while the second and third authors were staying at Kavli Institute for Theoretical Physics China, Beijing, in July and August, 2010; the authors were staying at National Center for Theoretical Sciences (South), Tainan, in September, 2010; and the first and third authors were staying at Academia Sinica, Taipei, in December, 2011. They are grateful to those institutes.
Article copyright: © Copyright 2018 American Mathematical Society