22 TABLE IV: The symmetry of the different configurations, trea ting the arrows as polar vectors, or as axial vectors with and without inclusion of the time reversal symmetry. In the last column we show the broken symmetry (we assume no magnetic field in the case of the 2 :2 collinear state and magnetic field along the z direction for 3:1 collinear and for the two canted states). The notation is the same as in the Table III, with the addition of two elements: σ v is a reflection to a plane perpendicular to the C ∞ axis ( σ xz is also a σ $_{v}$), while C ′ 2 is a two–fold rotation with axis perpendicular to the C ∞ axis. state polar vectors axial vectors spins (axial vectors + time reversal) symmetry broken 2:2 collinear D ∞ h = C ∞ ⊗ { 1 , C ′ $_{2}$, σ v , I } D ∞ h D ∞ h + Θ D ∞ h O (3) / ( O (2) × O (1)) = R P 2 3:1 collinear C ∞ v = C ∞ × { E, σ v } C ∞ × { E, I } C ∞ × { E, I } + Θ σ v C ∞ × { E, I } 1 2:2 canted C$_{2}$ v = { E, C$_{2}$ ( z ) , σ xz , σ yz } C$_{2}$$_{h}$ = { E, I, C$_{2}$ ( z ) , σ xy } C$_{2}$$_{h}$ + Θ σ xz C$_{2}$$_{h}$ C ∞ /C$_{2}$ 3:1 canted C$_{1}$$_{h}$ = { E, σ xz } S$_{2}$ = { E, I } S$_{2}$ + Θ σ xz S$_{2}$ C ∞