  We study the nonunitary diagonal cosets constructed from admissible
representations of Kac-Moody algebras at fractional level, with an emphasis on
the question of field identification. Generic classes of field identifications
are obtained from the analysis of the modular S matrix. These include the usual
class related to outer automorphisms, as well as some intrinsically nonunitary
field identifications. They allow for a simple choice of coset field
representatives where all field components of the coset are associated with
integrable finite weights.
