## Duke Mathematical Journal

Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

The central limit theorem for dependent random variablesVolume 15, Number 3 (1948)
On the critical values of $L$ -functions of $GL(2)$ and $GL(2) \times GL(2)$Volume 74, Number 2 (1994)
Kneading operators, sharp determinants, and weighted Lefschetz zeta functions in higher dimensionsVolume 124, Number 1 (2004)
Uniqueness of the blowup at isolated singularities for the Alt–Caffarelli functionalVolume 169, Number 8 (2020)
Connected Lie groups and property RDVolume 137, Number 3 (2007)
• ISSN: 0012-7094 (print), 1547-7398 (electronic)
• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 1935--
• Access: By subscription only
• Euclid URL: https://projecteuclid.org/dmj

### Featured bibliometrics

MR Citation Database MCQ (2018): 2.79
JCR (2018) Impact Factor: 2.199
JCR (2018) Five-year Impact Factor: 2.766
JCR (2018) Ranking: 15/314 (Mathematics)
Article Influence (2018): 4.346
Eigenfactor: Duke Mathematical Journal
SJR/SCImago Journal Rank (2018): 5.73

Indexed/Abstracted in: Current Contents: Physical, Chemical & Earth Sciences, IBZ Online, Magazines for Libraries, MathSciNet, Science Citation Index, Science Citation Index Expanded, Scopus, and zbMATH

### Featured article

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

Volume 169, Number 5 (2020)
##### Abstract

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 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 $G_{0}$ to realize the bijection as a deformation: for every irreducible tempered representation $\pi$ of G, we build, in an appropriate Fréchet space, a family of subspaces, and evolution operators that contract $\pi$ onto the corresponding representation of $G_{0}$.

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