  Recently a duality between a family of \mathcal{N}=2 supersymmetric higher
spin theories on AdS3, and the 't Hooft like limit of a class of Kazama-Suzuki
models (that are parametrised by N and k) was proposed. The higher spin
theories can be described by a Chern-Simons theory based on the
infinite-dimensional Lie algebra shs[\mu], and under the duality, \mu is to be
identified with \lambda=N/(N+k+1). Here we elucidate the structure of the
(quantum) asymptotic symmetry algebra sW_{\infty}[\mu] for arbitrary \mu and
central charge c. In particular, we show that for each value of the central
charge, there are generically four different values of \mu that describe the
same sW_{\infty} algebra. Among other things this proves that the quantum
symmetries on both sides of the duality agree; this equivalence does not just
hold in the 't Hooft limit, but even at finite N and k.
