  This work concerns the representation theory of the affine Lie algebra
$A_1^{(1)}$ at fractional level and its links to the representation theory of
the Virasoro algebra. We introduce affine Kac modules as certain finitely
generated submodules of Wakimoto modules. We conjecture the existence of
several classes of staggered $A_1^{(1)}$-modules and provide evidence in the
form of detailed examples. We extend the applicability of the
Goddard-Kent-Olive coset construction to include the affine Kac and staggered
modules. We introduce an exact functor between the associated category of
$A_1^{(1)}$-modules and the corresponding category of Virasoro modules. At the
level of characters, its action generalises the Mukhi-Panda residue formula. We
also obtain explicit expressions for all irreducible $A_1^{(1)}$-characters
appearing in the decomposition of Verma modules, re-examine the construction of
Malikov-Feigin-Fuchs vectors, and extend the Fuchs-Astashkevich theorem from
the Virasoro algebra to $A_1^{(1)}$.
