# Continuity of the Mackey-Higson bijection

@article{Afgoustidis2019ContinuityOT,
title={Continuity of the Mackey-Higson bijection},
author={Alexandre Afgoustidis and A. Aubert},
journal={arXiv: Representation Theory},
year={2019}
}
• Published 2019
• Mathematics
• arXiv: Representation Theory
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 $G_0$. In this short note, we collect some known facts about the topology of the tempered dual $\widetilde{G}$ and that of the unitary dual $\widehat{G_0}$, then verify that the Mackey-Higson bijection $\widetilde{G} \to \widehat{G_0}$ is continuous.
2 Citations

#### References

SHOWING 1-10 OF 15 REFERENCES
THE MACKEY ANALOGY AND K-THEORY
• 21
• Highly Influential
• PDF
T
• Crisp & N. Higson – “Parabolic induction and restriction via C∗-algebras and Hilbert C∗-modules”, Compos. Math. 152
• 2016