The usual approach to study 2d CFT relies on the Virasoro algebra and its representation theory. Moving away from the criticality, this infinite dimensional symmetry is lost so it is useful to have a look at 2d CFTs from more general framework of quantum integrability.
Every 2d conformal field theory has a natural infinite dimensional family of commuting higher spin Hamiltonians that can be constructed out of Virasoro generators. Perhaps surprisingly two different sets of Betheansatz equations are known that be used to diagonalize these (one by Bazhanov-Lukyanov-Zamolodchikov and another by Litvinov). I want to discuss these constructions as well as their relation to W algebras and the affine Yangian symmetry.