The CP^N Kazama-Suzuki models with the non-linear chiral algebra
SW_infinity[lambda] have been conjectured to be dual to the fully
supersymmetric Prokushkin-Vasiliev theory of higher-spin gauge fields coupled
to two massive N=2 multiplets on AdS_3. We perform a non-trivial check of this
duality by computing three-point functions containing one higher-spin gauge
field for arbitrary spin s and deformation parameter lambda from the bulk
theory, and from the boundary using a free ghost system based on the linear
sw_infinity[lambda] algebra. We find an exact match between the two
computations. In the 't Hooft limit, the three-point functions only depend on
the wedge subalgebra shs[lambda] and the results are equivalent for any theory
with such a subalgebra. In the process we also find the emergence of N=2
superconformal symmetry near the AdS_3 boundary by computing holographic OPE's,
consistently with a recent analysis of asymptotic symmetries of higher-spin
supergravity.Comment: 40 pages; This work is based on the first author's MSc thesis,
submitted to the Niels Bohr Institute, University of Copenhagen, in November
2012. v2: References added. v3: Minor typos fixe
