Topology of unitary dual of nonarchimedean GL(n)
type: Item
instance of: scholarly article
title: Topology of unitary dual of nonarchimedean GL(n)
zbMATH Open document ID: 0668.22006
DOI: 10.1215/S0012-7094-87-05522-0
author: Marko Tadić
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Let G be a locally compact group. The set of all equivalence classes of irreducible unitary representations of G is denoted by \(\hat G.\) The set \(\hat G\) is called the unitary dual of G and it carries a natural topology. Let F be a local nonarchimedean field. In this paper we consider properties of the representation theory of GL(n,F)-groups related to the topology of the unitary dual of GL(n,F). The main results of this paper are: classification of all isolated points modulo center in \(GL(n,F)^{\wedge}\), description of composition factor of ends of complementary series representations and description of \(GL(n,F)^{\wedge}\) as (abstract) topological space.
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 4093798
zbMATH Keywords: locally compact group
zbMATH Keywords: irreducible unitary representations
zbMATH Keywords: unitary dual
zbMATH Keywords: local nonarchimedean field
zbMATH Keywords: isolated points
zbMATH Keywords: complementary series representations
MaRDI profile type: Publication
cites work: All reductive \(\mathfrak p\)-adic groups are tame
cites work: Q3328755
cites work: Induced representations of reductive ${\germ p}$-adic groups. I
cites work: Computation of certain induced characters of P-adic groups
cites work: Q5562324
cites work: The structure of algebras of operator fields
cites work: Q3205463
cites work: Connection of the dual space of a group with the structure of its closed subgroups
cites work: Q5677723
cites work: Q5662170
cites work: Q5637115
cites work: Q5682814
cites work: Q4743014
cites work: On Certain L-Functions
cites work: Q4740108
cites work: Q3320612
cites work: Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)
cites work: Algèbres de Hecke et induites de représentations cuspidales, pour GL (N).
cites work: Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
cites work: Geometry of dual spaces of reductive groups (non-Archimedean case)
description: scientific article; zbMATH DE number 4093798