[en] Double superconducting transitions and the observed isotropy of the phase diagram; magnetic field (H) vs temperature (T) in a heavy Fermion compound UPt₃, are consistently accounted for by a scenario based on the one-dimensional representation (1D scenario) with odd-parity in the weak spin-orbit coupling case. A symmetry breaking field due to the antiferromagnetism (T_N = 5 K) lifts the spin space degeneracy of the pairing function to split the transition temperature T_c. The 1D scenario explains the experiments better than the previous 2D scenario based on the two-dimensional representation. The identified triplet pairing function of the B phase in low T and low H is characterized not only by time inversion breaking, but also by non-unitarity. In addition to the usual excitation branch with the line node, the existence of the gapless excitation branch in this state explains various long known puzzles, in particular, the 'residual' linear specific heat at low T. (author)