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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Parafermion vertex operator algebras and $W$-algebras
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by Tomoyuki Arakawa, Ching Hung Lam and Hiromichi Yamada PDF
Trans. Amer. Math. Soc. 371 (2019), 4277-4301 Request permission

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
  • MR Author ID: 611463
  • Email: arakawa@kurims.kyoto-u.ac.jp
  • Ching Hung Lam
  • Affiliation: Institute of Mathematics, Academia Sinica, Taipei 115, Taiwan
  • MR Author ID: 363106
  • Email: chlam@math.sinica.edu.tw
  • Hiromichi Yamada
  • Affiliation: Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan
  • MR Author ID: 232024
  • Email: yamada.h@r.hit-u.ac.jp
  • 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.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 4277-4301
  • MSC (2010): Primary 17B69; Secondary 17B65
  • DOI: https://doi.org/10.1090/tran/7547
  • MathSciNet review: 3917223