The restriction of a principal series to the maximal compact subgroup K = SU(2) of G can also be realized as an induced representation of K using the identification G / B = K / T, where T = B ∩ K is the maximal torus in K consisting of diagonal matrices with | z | = 1. It is the representation induced from the 1-dimensional representation z T, and is independent of ν. By Frobenius reciprocity, on K they decompose as a direct sum of the irreducible representations of K with dimensions | k | + 2 m + 1 with m a non-negative integer.