Modularity of Admissible-Level sl3 Minimal Models with Denominator 2

Abstract

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 u⩾3 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 degene..