We point out that the inequality det E > 0 distinguishes the kinematic
aI phase space of canonical connection gravity from that of a gauge fi
eld theory, and characterize the eigenvectors with positive, negative
and zero-eigenvalue of the corresponding quantum operator in a lattice
-discretized version of the theory. The diagonalization of <(det E)ove
r cap> is simplified by classifying its eigenvectors according to the
irreducible representations of the octagonal group. (C) 1997 Published
by Elsevier Science B.V.