Abstract
Recently a duality between a family of 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, is to be
identified with łambda=N/(N+k+1). Here we elucidate the structure of the
(quantum) asymptotic symmetry algebra sW\_ınfty\mu for arbitrary and
central charge c. In particular, we show that for each value of the central
charge, there are generically four different values of that describe the
same sW\_ınfty 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.
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