  We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of
two-sided BGG resolutions of G-integrable admissible representations of affine
Kac-Moody algebras at fractional levels. As an application we establish the
semi-infintie analogue of the generalized Borel-Weil theorem for mimimal
parabolic subalgebras which enables an inductive study of admissible
representations.
