## 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.

Cohomologically induced distinguished representations and cohomological test vectorsVolume 168, Number 1 (2019)
Cluster algebras III: Upper bounds and double Bruhat cellsVolume 126, Number 1 (2005)
Existence and deformations of Kähler–Einstein metrics on smoothable $\mathbb{Q}$ -Fano varietiesVolume 165, Number 16 (2016)
On Eisenstein series of half-integral weightVolume 52, Number 2 (1985)
The Noether inequality for algebraic $3$ -foldsVolume 169, Number 9 (2020)
• 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 (2019) Impact Factor: 2.194
JCR (2019) Five-year Impact Factor: 2.623
JCR (2019) Ranking: 18/324 (Mathematics)
Article Influence (2019): 4.103
Eigenfactor: Duke Mathematical Journal
SJR/SCImago Journal Rank (2019): 4.907

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### 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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