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}
}
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. 
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References

SHOWING 1-10 OF 15 REFERENCES
A description of the topology on the dual spaces of certain locally compact groups
  • 32
  • PDF
THE MACKEY ANALOGY AND K-THEORY
  • 21
  • Highly Influential
  • PDF
Les C*-algèbres et leurs représentations ..
  • 1,496
T
  • Crisp & N. Higson – “Parabolic induction and restriction via C∗-algebras and Hilbert C∗-modules”, Compos. Math. 152
  • 2016
...
1
2
...