  The principal admissible representations of affine Kac-Moody algebras are
studied, with a view to their use in conformal field theory. We discuss the
generation of the set of principal admissible highest weights, concentrating
mainly on $A_r^{(1)}$ at rational level $k$. A related algorithm is described
that produces the Malikov-Feigen-Fuchs null vectors of these representations.
With the principal admissible description of the highest weights, we are able
to prove that field identifications (including maverick ones) lead to the
canonical description of the primary fields of the nonunitary diagonal coset
theories.
