2024/06/15 by Justine Fasquel, Christopher Raymond, Fasquel, Justine +3
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Geometry and complex manifolds #Advanced Mathematical Physics Problems
paper · pdf · doi:10.48550/arxiv.2406.10646
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 \mathfraksl3 at level k = -3+(u)/(2), 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 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.