BGG reciprocity for current algebras

Current algebras are special maximal parabolic subalgebras of affine Lie algebras. In the case of untwisted affine Lie algebras they are isomorphic to the tensor product of a finite dimensional simple Lie algebra and the ring pf polynomials in one variable. The category of finite dimensional representations of current algebras is not semisimple. Recently Chari and collaborators have conjectured a version of the BGG reciprocity in this context, which connects simple finite dimensional representations, their projective covers, and standard modules. I will present a proof of this conjecture.