On quotient measures and induced representations
Let G be a locally compact group and H a closed subgroup of G. A function \(\rho\) : \(G\to {\mathbb{C}}\) is called a \(\rho\)-function if it satisfies the condition \(\rho (hg)=\delta (h)\Delta (h)^{-1}\rho (g)\) for all \(h\in H\) and \(g\in G\), where \(\delta\) and \(\Delta\) are the modular functions of H and G respectively. The author shows the existence of continuous \(\rho\)-functions and, as a consequence, positive Radon measures m on the quotient space whose translates \(m_ g\) have continuous Radon-Nikodym derivatives with respect to m. This observation allows a somewhat simpler proof of Mackey's intertwining theorem on induced representations.
Mackey's intertwining theorem on induced representations
scientific article; zbMATH DE number 4109335