  We generalise the analysis carried out in [arXiv:0710.5796], and find that
our previous results can be extended beyond the case of SL(N,C). In particular,
we show that an equivalence--at the level of the holomorphic chiral
algebra--between a bosonic string on a smooth coset manifold G/B and a B-gauged
version of itself on G, will imply an isomorphism of classical W-algebras and a
level relation which underlie a geometric Langlands correspondence for the
simply-laced, complex ADE-groups. In addition, as opposed to line operators and
branes of an open topological sigma-model, the Hecke operators and Hecke
eigensheaves, can, instead, be physically interpreted in terms of the
correlation functions of local operators in the holomorphic chiral algebra of a
closed, quasi-topological sigma-model. Our present results thus serve as an
alternative physical interpretation--to that of an electric-magnetic duality of
four-dimensional gauge theory demonstrated earlier by Kapustin and Witten in
[arXiv:hep-th/0604151]--of the geometric Langlands correspondence for complex
ADE-groups. The cases with tame and mild "ramifications" are also discussed.
