Admissible-level $$\mathfrak {sl}_3$$ minimal models

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 irreducible weight modules minimal model vertex operator algebra $${\textsf {L} }_{{\textsf {k} }}(\mathfrak {sl}_{3})$$ , when level }$$ is admissible. These are naturally described terms families parametrised by up two complex numbers. We also determine action relevant group automorphisms $$\widehat{\mathfrak {sl}}_{3}$$ on their isomorphism classes compute explicitly decomposition into irreducibles a given family’s parameters permitted take certain limiting values. Along with character formulae, previously established (Adv 393:108079, 2021. arXiv:2003.10148 [math.RT]), these results form input data required standard module formalism consistently modular transformations and, assuming validity natural conjecture, Grothendieck fusion coefficients admissible-level $$\mathfrak {sl}_{3}$$ models. second applies }=-\frac{3}{2}$$ . This gives nontrivial test for nonrational rank greater than 1 confirms expectation that methodology developed here will apply much generality.