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Abstract
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When
is a real
reductive group and
is its Cartan motion group, the Mackey–Higson bijection is a natural
one-to-one correspondence between all irreducible tempered representations of
and all irreducible unitary
representations of
.
We collect some known facts about the topology of the tempered dual
and that of the
unitary dual
,
and then verify that the Mackey–Higson bijection
is
continuous.
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Keywords
real reductive groups, Cartan motion group, tempered
representations, Fell topology, Mackey–Higson bijection
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Mathematical Subject Classification 2010
Primary: 22E47
Secondary: 22E50
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Milestones
Received: 8 November 2019
Revised: 16 November 2020
Accepted: 9 December 2020
Published: 8 March 2021
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