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Admissible-level sl3 minimal models

Kawasetsu, Kazuya, Ridout, David and Wood, Simon ORCID: 2022. Admissible-level sl3 minimal models. Letters in Mathematical Physics 112 (5) , 96. 10.1007/s11005-022-01580-9

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The first part of this work uses the algorithm recently detailed in Kawasetsu and Ridout (Commun Contemp Math 24:2150037, 2022. arXiv:1906.02935 [math.RT]) to classify the irreducible weight modules of the minimal model vertex operator algebra Lk(sl3), when the level k is admissible. These are naturally described in terms of families parametrised by up to two complex numbers. We also determine the action of the relevant group of automorphisms of slˆ3 on their isomorphism classes and compute explicitly the decomposition into irreducibles when a given family’s parameters are permitted to take certain limiting values. Along with certain character formulae, previously established in Kawasetsu (Adv Math 393:108079, 2021. arXiv:2003.10148 [math.RT]), these results form the input data required by the standard module formalism to consistently compute modular transformations and, assuming the validity of a natural conjecture, the Grothendieck fusion coefficients of the admissible-level sl3 minimal models. The second part of this work applies the standard module formalism to compute these explicitly when k=−32. This gives the first nontrivial test of this formalism for a nonrational vertex operator algebra of rank greater than 1 and confirms the expectation that the methodology developed here will apply in much greater generality.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Mathematics
Publisher: Springer
ISSN: 0377-9017
Date of First Compliant Deposit: 27 September 2022
Date of Acceptance: 21 August 2022
Last Modified: 18 Nov 2023 20:33

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