  Given a representation of a unimodular locally compact group, we discuss
criteria for associated coherent state expansions in terms of the commuting
algebra. It turns out that for those representations that admit such expansions
there exists a unique finite trace on the commuting algebra such that the
admissible vectors are precisely the tracial vectors for that trace. This
observation is immediate from the definition of the group Hilbert algebra and
its associated trace. The trace criterion allows to discuss admissibility in
terms of the central decomposition of the regular representation. In
particular, we present a new proof of the admissibility criteria derived for
the type I case. In addition we derive admissibility criteria which generalize
the Wexler-Raz biorthogonality relations characterizing dual windows for
Weyl-Heisenberg frames.
