Imposing det E>0 in discrete quantum gravity

We point out that the inequality det E > 0 distinguishes the kinematicaI phase space of canonical connection gravity from that of a gauge field 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)over cap> is simplified by classifying its eigenvectors according to the irreducible representations of the octagonal group. (C) 1997 Published by Elsevier Science B.V.