An irreducible representation of this group of operators is furnished by the Wigner D-matrix : D m ′ m s ( α α , β β , γ γ ) ≡ ≡ ⟨ ⟨ s m ′ | R ( α α , β β , γ γ ) | s m ⟩ ⟩ = e − − i m ′ α α d m ′ m s ( β β ) e − − i m γ γ , where d m ′ m s ( β β ) = ⟨ ⟨ s m ′ | e − − i β β s y | s m ⟩ ⟩ is Wigner's small d-matrix. Note that for γ = 2π and α = β = 0 ; i.e., a full rotation about the z axis, the Wigner D-matrix elements become D m ′ m s ( 0 , 0 , 2 π π ) = d m ′ m s ( 0 ) e − − i m 2 π π = δ δ m ′ m ( − − 1 ) 2 m .