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Transactions of the American Mathematical Society

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The irreducible modules and fusion rules for the parafermion vertex operator algebras


Authors: Chunrui Ai, Chongying Dong, Xiangyu Jiao and Li Ren
Journal: Trans. Amer. Math. Soc. 370 (2018), 5963-5981
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/tran/7302
Published electronically: November 14, 2017
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Abstract: The irreducible modules for the parafermion vertex operator algebra associated to any finite dimensional Lie algebra $ \mathfrak{g}$ and any positive integer $ k$ are classified, the quantum dimensions are computed and the fusion rules are determined.


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Chunrui Ai
Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China–and–School of Mathematics and Statistics, Zhengzhou University, Henan 450001, People’s Republic of China
Email: aichunrui0908@126.com

Chongying Dong
Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
Email: dong@ucsc.edu

Xiangyu Jiao
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China
Email: xyjiao@math.ecnu.edu.cn

Li Ren
Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China
Email: renl@scu.edu.cn

DOI: https://doi.org/10.1090/tran/7302
Received by editor(s): November 1, 2016
Received by editor(s) in revised form: March 30, 2017
Published electronically: November 14, 2017
Additional Notes: The first author was supported by National Science Foundation for Postdoctoral Science of China (No. 2017M612409)
The second author was supported by NSF grant DMS-1404741 and China NSF grant 11371261
The third author was partially supported by China NSF grants 11401213 and Natural Science Foundation of Shanghai 13DZ2260400
The fourth author was supported by China NSF grants 11301356 and 11671277
Article copyright: © Copyright 2017 American Mathematical Society

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