  It was recently proposed that a large N limit of a family of minimal model
CFTs is dual to a certain higher spin gravity theory in AdS_3, where the 't
Hooft coupling constant of the CFT is related to a deformation parameter of the
higher spin algebra. We identify the asymptotic symmetry algebra of the higher
spin theory for generic 't Hooft parameter, and show that it coincides with a
family of W-algebras previously discovered in the context of the KP hierarchy.
We furthermore demonstrate that this family of W-algebras controls the
representation theory of the minimal model CFTs in the 't Hooft limit. This
provides a non-trivial consistency check of the proposal and explains part of
the underlying mechanism.
