We show a physical realization of the Langlands duality in correlation
functions of H_3^+ WZNW model. We derive a dual version of the
Stoyanovky-Riabult-Teschner (SRT) formula that relates the correlation function
of the H_3^+ WZNW and the dual Liouville theory to investigate the level
duality k-2 \to (k-2)^{-1} in the WZNW correlation functions. Then, we show
that such a dual version of the H_3^+ - Liouville relation can be interpreted
as a particular case of a biparametric family of non-rational CFTs based on the
Liouville correlation functions, which was recently proposed by Ribault. We
study symmetries of these new non-rational CFTs and compute correlation
functions explicitly by using the free field realization to see how a
generalized Langlands duality manifests itself in this framework. Finally, we
suggest an interpretation of the SRT formula as realizing the Drinfeld-Sokolov
Hamiltonian reduction. Again, the Hamiltonian reduction reveals the Langlands
duality in the H_3^+ WZNW model. Our new identity for the correlation functions
of H_3^+ WZNW model may yield a first step to understand quantum geometric
Langlands correspondence yet to be formulated mathematically.