  We study the two-dimensional twisted (0,2) sigma-model on various smooth
complex flag manifolds G/B, and explore its relevance to the geometric
Langlands program. We find that an equivalence - at the level of the
holomorphic chiral algebra - between a bosonic string on 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
G=SL(N,C). This furnishes an alternative physical interpretation of the
geometric Langlands correspondence for G=SL(N,C), to that demonstrated earlier
by Kapustin and Witten via an electric-magnetic duality of four-dimensional
gauge theory. Likewise, the Hecke operators and Hecke eigensheaves will have an
alternative physical interpretation in terms of the correlation functions of
local operators in the holomorphic chiral algebra of a quasi-topological
sigma-model without boundaries. A forthcoming paper will investigate the
interpretation of a ``quantum'' geometric Langlands correspondence for
G=SL(N,C) in a similar setting, albeit with fluxes of the sigma-model moduli
which induce a ``quantum'' deformation of the relevant classical algebras
turned on.
