Two-sided BGG resolutions of admissible representations (Q2922914)

Let \(\mathfrak{g}\) be an affine Kac-Moody algebra and \(\mathfrak{a}\) the classical part of \(\mathfrak{g}\). In this paper, for any \(\mathfrak{a}\)-integrable admissible representation \(V\) of \(\mathfrak{g}\), the author proves existence of a complex of Wakimoto modules whose homology at position zero is isomorphic to \(V\) and is zero at all non-zero positions. As a special case, this gives a proof to a conjecture by Frenkel, Kac and Wakimoto on existence of such resolution for principle admissible representations.NEWLINENEWLINEAs an application, a semi-infinite analogue of the generalized Borel-Weyl theorem for minimal parabolic subalgebras is established.