Twisted actions and the obstruction to extending unitary representations of subgroups

2003/09/24 by Astrid an Huef, Huef, Astrid an, Iain Raeburn +1
Mathematics · #20C99 #22D10 #22D25 #46L10 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.OA #math.RT #msc:20C99 #msc:22D10 #msc:22D25 #msc:46L10

paper · pdf · doi:10.48550/arxiv.math/0309396

arxiv created 2003/09/24 · openalex publication_date 2003/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that G is a locally compact group and π is a (not necessarily irreducible) unitary representation of a closed normal subgroup N of G on a Hilbert space H. We extend results of Clifford and Mackey to determine when π extends to a unitary representation of G on the same space H in terms of a cohomological obstruction.

Citations

• A Categorical Approach to Imprimitivity Theorems for C*-Dynamical Systems

Related

• Extension problems and non-abelian duality for C^*-algebras
• Weak containment by restrictions of induced representations
• Twisted GGP Problems and Conjectures
• Extension problems for representations of crossed-product C*-algebras
• Induced representations of infinite-dimensional groups