  We explore some aspects of three-dimensional higher-spin holography by
studying scalar fluctuations in the background of higher-spin black holes. We
furnish an independent derivation of the bulk-boundary propagator by purely
invoking a well-known infinite dimensional matrix representation of
$hs[\lambda]$ algebra related to its construction as a quotient of the
universal enveloping algebra of $sl(2)$, thus evading the need in previous
literature to perform an analytic continuation from some integer to $\lambda$.
The propagator and the boundary two-point functions are derived for black hole
solutions in $hs[\lambda]\times hs[\lambda]$ Chern-Simons theory with spin-3
and spin-4 charges up to second-order in the potentials. We match them with
three- and four-point torus correlation functions of the putative dual
conformal field theory which has $\mathcal{W}_\infty [\lambda]$ symmetry and is
deformed by higher-spin currents.
