Geometry of dual spaces of reductive groups (non-Archimedean case)

DOI10.1007/BF02791122zbMath0664.22010MaRDI QIDQ1115542

Marko Tadić

Publication date: 1988

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

composition factorsdual groupsisolated pointsunitarizable representationsconnected reductive groupBernstein centernonarchimedean local fieldcomplementary series representationsirreducible smooth representationdual spaces of reductive groupsunitary dual space

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50)

Related Items (18)

Topology of unitary dual of nonarchimedean GL(n) ⋮ The unitary dual of \(p\)-adic \(G_2\) ⋮ Unnamed Item ⋮ The Local Langlands Conjecture for ⋮ Unitarizability in Corank Three for Classical 𝑝-adic Groups ⋮ The Tadić philosophy: an overview of the guiding principles and underlying ideas in the work of Marko Tadić ⋮ On tempered and square integrable representations of classical \(p\)-adic groups ⋮ The Trace Formula and the Proof of the Global Jacquet-Langlands Correspondence ⋮ Unitary representations of \(p\)-adic \(U(5)\) ⋮ The Langlands dual and unitary dual of quasi-split 𝑃𝐺𝑆𝑂₈^{𝐸} ⋮ COMPARISON OF LOCAL RELATIVE CHARACTERS AND THE ICHINO–IKEDA CONJECTURE FOR UNITARY GROUPS ⋮ Generalized spherical functions on reductive 𝑝-adic groups ⋮ On geometric density of Hecke eigenvalues for certain cusp forms ⋮ Modular forms on non-linear double covers of algebraic groups ⋮ An external approach to unitary representations ⋮ Plancherel formula for \(\mathrm{GL}_n(F)\setminus \mathrm{GL}_n(E)\) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups ⋮ Supercuspidal representations: An exhaustion theorem ⋮ Compatible systems of symplectic Galois representations and the inverse Galois problem. III: Automorphic construction of compatible systems with suitable local properties

Cites Work

• On the unitarizability of derived functor modules
• Proof of a conjecture of Bernstein
• Trace Paley-Wiener theorem for reductive p-adic groups
• Topology of unitary dual of nonarchimedean GL(n)
• The unitary dual of \(Gl(3,R)\) and \(Gl(4,R)\)
• All reductive \(\mathfrak p\)-adic groups are tame
• The Langlands quotient theorem for p-adic groups
• Asymptotic properties of unitary representations
• Unitary representations of Gl(n,R) with non-trivial (g,K)-cohomology
• Unitarizability of certain series of representations
• Non-unitary dual spaces of groups
• Connection of the dual space of a group with the structure of its closed subgroups
• Introduction to Harmonic Analysis on Reductive P-adic Groups. (MN-23): Based on lectures by Harish-Chandra at The Institute for Advanced Study, 1971-73
• On Euler Products and the Classification of Automorphic Representations I
• Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)
• The Dual Spaces of Banach Algebras
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