Year: 2026
Type: preprint
Abstract: The topological $1$-bounded entropy $h^\text{top}(C^*(Γ))$ of the full group $C^*$-algebra of a finitely generated group $Γ$ is given a representation-theoretic interpretation. The implications of Hilbert-Schmidt stability and matricial stability are investigated within this setting, recovering and strengthening a representation growth result of Hadwin and Shulman. The entropy framework is used to prove upper bounds on representation growth for superrigid groups and property (T) groups. This recovers a result of De La Harpe, Robinson, and Valette on the growth rate of the irreducible unitary representations of a property (T) group within the framework of $1$-bounded entropy. A soft proof that $SL_n(\Z)$ admits subexponential representation growth is recorded.
Source: arXiv (Cornell University)
Author: MacMahon, Connor
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7222733507