Free Group Representations from Vector-Valued Multiplicative Functions, II

2015/01/13 by M. Gabriella Kuhn, Kuhn, M. Gabriella, Sandra Saliani +3
Mathematics · #15B48 #22D10 #22D25 #43A35 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Primary: 43A65 #Representation Theory (math.RT) #Secondary: 15A42 #math.RT #msc:15A42 #msc:15B48 #msc:22D10 #msc:22D25 #msc:43A35 #msc:43A65

paper · pdf · doi:10.48550/arxiv.1501.03103

arxiv created 2015/01/13 · openalex publication_date 2015/01/13 · arxiv updated 2015/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ be a non-commutative free group on finitely many generators. In a previous work two of the authors have constructed the class of multiplicative representations of Γ and proved them irreducible as representation of Γ\ltimes_λC(Ω). In this paper we analyze multiplicative representations as representations of Γ and we prove a criterium for irreducibility based on the growth of their matrix coefficients.

Related

• Free group representations from vector-valued multiplicative functions, III
• Stability properties of multiplicative representations of free groups
• Some irreducible free group representations in which a linear combination of the generators has an eigenvalue
• Free group representations: duplicity on the boundary
• Multipliers and lacunary sets in non-amenable groups