The principal series, or unitary principal series, are the unitary representations induced from the one-dimensional representations of the lower triangular subgroup B of G = SL ( 2 , C ) . Since the one-dimensional representations of B correspond to the representations of the diagonal matrices, with non-zero complex entries z and z, they thus have the form χ χ ν ν , k ( z 0 c z − − 1 ) = r i ν ν e i k θ θ , for k an integer, ν real and with z = re. The representations are irreducible ; the only repetitions, i.e. isomorphisms of representations, occur when k is replaced by − k. By definition the representations are realized on L sections of line bundles on G / B = S 2 , which is isomorphic to the Riemann sphere. When k = 0, these representations constitute the so-called spherical principal series.