  We indicate how to introduce chemical potentials for higher spin charges in
higher spin anti-de Sitter gravity in a manner that manifestly preserves the
original asymptotic W-symmetry. This is done by switching on a non-vanishing
component of the connection along the temporal (thermal) circles. We first
recall the procedure in the pure gravity case (no higher spin) where the only
"chemical potentials" are the temperature and the chemical potential associated
with the angular momentum. We then generalize to the higher spin case. We find
that there is no tension with the W(N) or W(infinity) asymptotic algebra, which
is obviously unchanged by the introduction of the chemical potentials. Our
argument is non-perturbative.
