  Using a dimensional reduction formula for the lattice fermion determinant we
study canonical determinants on quenched SU(3) gauge configurations. The
canonical determinants decribe a fixed quark number and we analyze their
properties below and above the transition temperature. We find that above $T_c$
the signatures of center symmetry breaking are very strongly manifest in the
distribution of the canonical determinants in the complex plane, and we discuss
possible physical implications of this finding. We furthermore analyze the
relative weight of the different quark sectors below and above the transition
temperature.
