Two-sided BGG resolutions of admissible representations

Abstract

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