On characters of irreducible unitary representations of general linear groups
type: Item
instance of: scholarly article
title: On characters of irreducible unitary representations of general linear groups
zbMATH Open document ID: 0856.22026
DOI: 10.1007/BF02953339
author: Marko Tadić
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1997-02-03T00:00:00Z
review text: The author reduces the determination of the characters of irreducible unitary representations of \(\text{GL}(n)\) over a non-Archimedean local field to the determination of the characters of the irreducible square integrable representations of \(\text{GL}(m)\) with \(m\leq n\). He also obtains a formula expressing the characters of irreducible unitary representations in terms of the characters of the segment representations of Zelevinsky. This formula generalizes the classical formula for the Steinberg character of \(\text{GL}(n)\). To obtain his results, he uses a clever trick based on the formal similarity of the unitary duals in the Archimedean and the non-Archimedean case and a result of Gregg Zuckerman expressing the character of the trivial representation as a linear combination of standard characters for \(\text{GL}(n)\) over complex numbers.
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 878390
zbMATH Keywords: general linear group
zbMATH Keywords: characters
zbMATH Keywords: irreducible unitary representations
zbMATH Keywords: local field
zbMATH Keywords: Steinberg character
reviewed by: Dragan Milicic
MaRDI profile type: Publication
cites work: Q3328755
cites work: Q3885948
cites work: The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129)
cites work: Q4777531
cites work: Characters and Jacquet modules
cites work: A Construction of the Supercuspidal Representations of GL n (F), F p-Adic
cites work: Degrees and formal degrees for division algebras and \(GL_ n\) over a p- adic field
cites work: Computation of certain induced characters of P-adic groups
cites work: Q3241249
cites work: Q4129655
cites work: Character Formulas for Supercuspidal Representations of GL ℓ , ℓ a Prime
cites work: \({\mathcal D}\)-elliptic sheaves and the Langlands correspondence
cites work: Q5682814
cites work: Q3724585
cites work: Q4743014
cites work: Jordan algebras and degenerate principal series.
cites work: Q3488334
cites work: Analysis in matrix spaces and some new representations of \(SL(N,\mathbb{C})\)
cites work: Unitary dual of 𝑝-adic 𝐺𝐿(𝑛). Proof of Bernstein conjectures
cites work: Proof of a conjecture of Bernstein
cites work: Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)
cites work: Topology of unitary dual of nonarchimedean GL(n)
cites work: Induced representations of GL (n, A) for p-adic division algebras A.
cites work: An external approach to unitary representations
cites work: Q4729995
cites work: The unitary dual of \(\mathrm{GL}(n)\) over an archimedean field
cites work: Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
description: scientific article; zbMATH DE number 878390