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Article Dans Une Revue Duke Mathematical Journal Année : 2020

On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representations

Résumé

Attached to any reductive Lie group $G$ is a "Cartan motion group" $G_0$ $-$ a Lie group with the same dimension as $G$, but a simpler group structure. A natural one-to-one correspondence between the irreducible tempered representations of $G$ and the unitary irreducible representations of $G_0$, whose existence had been suggested by Mackey in the 1970s, has recently been described by the author. In the present notes, we use the existence of a family of groups interpolating between $G$ and $G_0$ to realize the bijection as a deformation: for every irreducible tempered representation $\pi$ of G, we build, in an appropriate Fr\'echet space, a family of subspaces and evolution operators that contract $\pi$ onto the corresponding representation of $G_0$.

Dates et versions

hal-01967750 , version 1 (01-01-2019)

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Citer

Alexandre Afgoustidis. On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representations. Duke Mathematical Journal, 2020, 169 (5), pp.897-960. ⟨10.1215/00127094-2019-0071⟩. ⟨hal-01967750⟩
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