Equivalence Classes of Boundary Conditions in Gauge Theory on $Z_3$ Orbifold

We study equivalence classes of boundary conditions in gauge theory on the orbifold $T^2\mathrm{/}{Z}_3$. Orbifold conditions and those gauge transformation properties are given and the gauge equivalence is understood by the Hosotani mechanism. Mode expansions are carried out for six-dimensional $Z_3$ singlet fields and a $Z_3$ triplet field, and the one-loop effective potential for Wilson line phases is calculated.