#### Vol. 310, No. 2, 2021

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Continuity of the Mackey–Higson bijection

### Alexandre Afgoustidis and Anne-Marie Aubert

Vol. 310 (2021), No. 2, 257–273
DOI: 10.2140/pjm.2021.310.257
##### Abstract

When $G$ is a real reductive group and ${G}_{0}$ 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 ${G}_{0}$. We collect some known facts about the topology of the tempered dual $\stackrel{˜}{G}$ and that of the unitary dual $\stackrel{̂}{{G}_{0}}$, and then verify that the Mackey–Higson bijection $\stackrel{˜}{G}\to \stackrel{̂}{{G}_{0}}$ is continuous.

##### Keywords
real reductive groups, Cartan motion group, tempered representations, Fell topology, Mackey–Higson bijection
Primary: 22E47
Secondary: 22E50