Admissible-level sl3 minimal models

Abstract

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 sl^ 3 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 ..