Mackey analogy via 𝒟-modules for SL(2, ℝ)

DOI10.1142/S0129167X17500550zbMath1372.22010arXiv1610.04103OpenAlexW2617155861MaRDI QIDQ4975371

Shilin Yu, Qijun Tan, Yi-Jun Yao

Publication date: 4 August 2017

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04103

zbMATH Keywords

\(\mathcal{D}\)-modulesadmissible representations of \(\mathrm{SL}(2,\mathbb{R})\)Mackey-Higson analogy

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46)

Related Items (4)

The algebraic Mackey-Higson bijections ⋮ On the analogy between real reductive groups and Cartan motion groups: contraction of irreducible tempered representations ⋮ Mackey analogy as deformation of \(\mathcal{D}\)-modules ⋮ Orbital integrals and \(K\)-theory classes

Cites Work

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• Localization and standard modules for real semisimple Lie groups. I: The duality theorem
• Classification of irreducible tempered representations of semisimple groups. I
• Special \(K\)-types, tempered characters and the Beilinson-Bernstein realization
• Representations of real reductive Lie groups
• On the analogy between real reductive groups and Cartan motion groups: contraction of irreducible tempered representations
• Intertwining operators and the representations of \(SL(2,R)\)
• Algebraic Families of Harish-Chandra Pairs
• On the Contraction of Groups and Their Representations

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