On the representation theory of the vertex algebra L−5/2(sl(4))

We study the representation theory of non-admissible simple affine vertex algebra [Formula: see text]. determine an explicit formula for singular vector conformal weight four in universal text], and show that it generates maximal ideal classify irreducible text]-modules category fusion rules between modules ordinary It turns out this is isomorphic to also prove text] a semi-simple, rigid braided tensor category. In our proofs, we use notion collapsing level text]-algebra, properties embedding at from D. Adamovic et al. [Finite vs infinite decompositions embeddings, Comm. Math. Phys. 348 (2016) 445–473.]. with respect subregular nilpotent element meaning quotient text]-algebra Heisenberg certain results on vanishing non-vanishing cohomology quantum Hamiltonian reduction functor are more subtle than case minimal reduction.