The even spin W^e_\infty algebra that is generated by the stress energy tensor together with one Virasoro primary field for every even spin s \geq 4 is analysed systematically by studying the constraints coming from the Jacobi identities. It is found that the algebra is characterised, in addition to the central charge, by one free parameter that can be identified with the self-coupling constant of the spin 4 field. We show that W^e_\infty can be thought of as the quantisation of the asymptotic symmetry algebra of the even higher spin theory on AdS_3. On the other hand, W^e_\infty is also quantum equivalent to the so(N) coset algebras, and thus our result establishes an important aspect of the even spin minimal model holography conjecture. The quantum equivalence holds actually at finite central charge, and hence opens the way towards understanding the duality beyond the leading 't Hooft limit.Comment: 32 pages, v2: reference added, minor changes in tex

For the N = 2 Kazama-Suzuki models that appear in the duality with a higher spin theory on AdS 3 it is shown that the large level limit can be interpreted as a continuous orbifold of 2N free bosons and fermions by the group U(N ). In particular, we show that the subset of coset representations that correspond to the perturbative higher spin degrees of freedom are precisely described by the untwisted sector of this U(N ) orbifold. We furthermore identify the twisted sector ground states of the orbifold with specific coset representations, and give various pieces of evidence in favour of this identification.

The large level limit of the N = 2 minimal models that appear in the duality with the N = 2 supersymmetric higher spin theory on AdS 3 is shown to be a natural subsector of a certain symmetric orbifold theory. We study the relevant decompositions in both the untwisted and the twisted sector, and analyse the structure of the higher spin representations in the twisted sector in some detail. These results should help to identify the string background of which the higher spin theory is expected to describe the leading Regge trajectory in the tensionless limit.