Modularity of admissible-level sl₃ minimal models with denominator 2

We use the newly developed technique of inverse quantum hamiltonian reduction to investigate the representation theory of the simple affine vertex algebra A₂ (u, 2) associated to sl₃ at level k = -3+u2, for u3 odd. Starting from the irreducible modules of the corresponding simple Bershadsky-Polyakov vertex operator algebras, we show that inverse reduction constructs all irreducible lower-bounded weight A₂ (u, 2) -modules. This proceeds by first constructing a complete set of coherent families of fully relaxed highest-weight A₂ (u, 2) -modules and then noting that the reducible members of these families degenerate to give all remaining irreducibles. Using this fully relaxed construction and the degenerations, we deduce modular S-transforms for certain natural generalised characters of these irreducibles and their spectral flows. With this modular data in hand, we verify that the (conjectural) standard Verlinde formula predicts Grothendieck fusion rules with nonnegative-integer multiplicities.