  We compute the algebras of self-extensions of the vacuum module and the Verma
modules over an affine Kac-Moody algebra g^ in suitable categories of
Harish-Chandra modules. We show that at the critical level these algebras are
isomorphic to the algebras of differential forms on various spaces of opers
associated to the Langlands dual Lie algebra of g, whereas away from the
critical level they become trivial. These results rely on and generalize the
description of the corresponding algebras of endomorphisms obtained by Feigin
and Frenkel and the description of the corresponding graded versions due to
Fishel, Grojnowski and Teleman.
