Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the analogy between real reductive groups and Cartan motion groups.
  I: The Mackey-Higson bijection   George Mackey suggested in 1975 that there should be analogies between the
irreducible unitary representations of a noncompact reductive Lie group $G$ and
those of its Cartan motion group $G_0$ $-$ the semidirect product of a maximal
compact subgroup of $G$ and a vector space. He conjectured the existence of a
natural one-to-one correspondence between "most" irreducible (tempered)
representations of $G$ and "most" irreducible (unitary) representations of
$G_0$. We here describe a simple and natural bijection between the tempered
duals of both groups, and an extension to a one-to-one correspondence between
the admissible duals.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org