Equivalence Classes of Boundary Conditions in SU(N) Gauge Theory on 2-dimensional Orbifolds

We study equivalence classes of boundary conditions in an SU(N) gauge theory on six-dimensional space-time including two-dimensional orbifold. For five kinds of two-dimensional orbifolds $S^1/Z_2 \times S^1/Z_2$ and $T^2/Z_m$ $(m=2,3,4,6)$, orbifold conditions and those gauge transformation properties are given and the equivalence relations among boundary conditions are derived. The classification of boundary conditions related to diagonal representatives is carried out using the equivalence relations.