Simple Modules for Affine Vertex Algebras in the Minimal Nilpotent Orbit

We explicitly construct, in terms of Gelfand-Tsetlin tableaux, a new family of simple positive energy representations for the simple affine vertex algebra V-k(sl(n+1)) in the minimal nilpotent orbit of sl(n+1). These representations are quotients of induced modules over the affine Kac-Moody algebra (sl) over cap (n+1) and include in particular all admissible simple highest weight modules and all simple modules induced from sl(2). Any such simple module in the minimal nilpotent orbit has bounded weight multiplicities.