Square integrable representations of unimodular groups

David S. Shucker

Type: Article

Publication Date: 1983-01-01

Citations: 13

DOI: https://doi.org/10.1090/s0002-9939-1983-0706534-4

Abstract

An elementary proof is given showing that if a continuous irreducible unitary representation of a locally compact unimodular group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has one nontrivial square integrable matrix entry, then all its matrix entries are square integrable. This result was first proved by R. Godement.

Locations

Proceedings of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Square Integrable Representations of Unimodular Groups	1983	David S. Shucker
+ PDF Chat	Square integrable representations and the Fourier algebra of a unimodular group	1977	Giancarlo Mauceri
+	A note on square-integrable representations	1970	Ray A. Kunze
+	A note on square-integrable representations	1975	John Phillips
+ PDF Chat	Square-integrable representations of non-unimodular groups	1976	Alan L. Carey
+	Square-Integrable Representations	2002	M. W. Wong
+	Realization of Square-Integrable Representations of Unimodular Lie Groups on L 2 -Cohomology Spaces	1980	Jacob Rosenberg
+	Appendix VII. Square Integrable Representations of Locally Compact Groups	2000
+ PDF Chat	ON THE SYMMETRY PROPERTIES OF POWERS OF REPRESENTATIONS OF THE TWO-DIMENSIONAL UNIMODULAR UNITARY GROUP	1954	F. D. Murnaghan
+	On the regular representation of a nonunimodular locally compact group	1976	Michel Duflo Calvin C. Moore
+	Square Integrable Representation of Groupoids	2006	Habib Amiri M. Lashkarizadeh Bami
+ PDF Chat	Square integrable representations of semisimple Lie groups	1974	Juan Tirao
+ PDF Chat	Square Integrable Representations of Nilpotent Groups	1973	Calvin C. Moore Joseph A. Wolf
+ PDF Chat	Square integrable representations of nilpotent groups	1973	Calvin C. Moore Joseph A. Wolf
+	Finite-dimensional representations of the group of unimodular matrices	1950	Israel M. Gelfand Michael .L. Zetlin
+	On the frobenius reciprocity theorem for square integrable representations of nonunimodular groups	1987	Ray A. Kunze
+ PDF Chat	Square-integrable representations of nilpotent groups	1973	Joseph A. Wolf Calvin C. Moore
+	Irreducible representations of the unitary group	2008	Jacques Faraut
+	An Inversion Formula for Integrable Coefficients of Unitary Representations of Locally Compact Groups	1982	潔池庄司
+	Square-integrable imprimitivity systems	2000	Gianni Cassinelli Ernesto De Vito Alberto Levrero

Works That Cite This (6)

Action	Title	Year	Authors
+	Irreducible Unitary Representations Concerning Homogeneous Holomorphic Line Bundles Over Elliptic Orbits	2018	Nobutaka Boumuki Tomonori Noda
+	Bibliography	1988
+	Square Integrable Representations, An Invaluable Tool	2018	Paolo Aniello
+	Bibliography	1988
+ PDF Chat	Quantum theory of unambiguous measurements	2009	Michal Sedlák
+	Quantum Harmonic Analysis on Locally Compact Abelian Groups	2025	Robert Fulsche Niklas Galke

Works Cited by This (1)

Action	Title	Year	Authors
+ PDF Chat	Représentations de Groupes Localement Compacts	1972	Armand Borel