  We study black holes carrying higher spin charge in AdS3 within the framework
of SL(N, R) x SL(N, R) Chern-Simons theory. Focussing attention on the N=4
case, we explicitly analyze the asymptotic symmetry algebra of black hole
solutions with a chemical potential for spin-four charge. We demonstrate that
the background describes an RG flow between an IR fixed point with W_4 symmetry
and a UV fixed point with W-symmetry associated to a non-principal embedding of
sl(2) in sl(4). Matching Chern-Simons equations with Ward identities of the
deformed CFT, we show that the UV stress tensor is twisted by a certain U(1)
current, and the flow is triggered by an operator with dimension 4/3 at the UV
fixed point. We find independent confirmation of this picture via a consistent
formulation of thermodynamics with respect to this UV fixed point. We further
analyze the thermodynamics of multiple branches of black hole solutions for
N=4,5 and find that the BTZ-branch, dominant at low temperatures, ceases to
exist at higher temperatures following a merger with a thermodynamically
unstable branch. We also point out an interesting connection between the RG
flows and generalized KdV hierarchies.
