CONTINUITY OF THE MACKEY-HIGSON BIJECTION

When G is a real reductive group and G₀ is its Cartan motion group, the Mackey-Higson bijection is a natural one-to-one correspondence between all irreducible tempered representations of G and all irreducible unitary representations of G₀. We collect some known facts about the topology of the tempered dual (Formula presented) and that of the unitary dual (Formula presented), and then verify that the Mackey–Higson bijection (Formula presented) is continuous.