  Based on the permutation group formalism, we present a discrete symmetry
algebra in QCD. The discrete algebra is hidden symmetry in QCD, which is
manifest only on a space-manifold with non-trivial topology. Quark confinement
in the presence of the dynamical quarks is discussed in terms of the discrete
symmetry algebra. It is shown that the quark deconfinement phase has the ground
state degeneracy depending on the topology of the space, which gives a
gauge-invariant distinction between the confinement and deconfinement phases.
We also point out that new quantum numbers relating to the fractional quantum
Hall effect exist in the deconfinement phase.
