Invariant subalgebras of affine vertex algebras

AbstractGiven a finite-dimensional complex Lie algebra g equipped with a nondegenerate, symmetric, invariant bilinear form B, let Vk(g,B) denote the universal affine vertex algebra associated to g and B at level k. For any reductive group G of automorphisms of Vk(g,B), we show that the invariant subalgebra Vk(g,B)G is strongly finitely generated for generic values of k. This implies the existence of a new family of deformable W-algebras W(g,B,G)k which exist for all but finitely many values of k