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1 April 2020 On the analogy between real reductive groups and Cartan motion groups: Contraction of irreducible tempered representations
Alexandre Afgoustidis
Duke Math. J. 169(5): 897-960 (1 April 2020). DOI: 10.1215/00127094-2019-0071

Abstract

Attached to any reductive Lie group G is a “Cartan motion group” G0—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 G0, whose existence was suggested by Mackey in the 1970s, has recently been described by the author. In the present article, we use the existence of a family of groups interpolating between G and G0 to realize the bijection as a deformation: for every irreducible tempered representation π of G, we build, in an appropriate Fréchet space, a family of subspaces, and evolution operators that contract π onto the corresponding representation of G0.

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Alexandre Afgoustidis. "On the analogy between real reductive groups and Cartan motion groups: Contraction of irreducible tempered representations." Duke Math. J. 169 (5) 897 - 960, 1 April 2020. https://doi.org/10.1215/00127094-2019-0071

Information

Received: 24 September 2018; Revised: 29 August 2019; Published: 1 April 2020
First available in Project Euclid: 6 February 2020

zbMATH: 07198468
MathSciNet: MR4079418
Digital Object Identifier: 10.1215/00127094-2019-0071

Subjects:
Primary: 22E46
Secondary: 22E45

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 5 • 1 April 2020
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