Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 29 min ago
PreprintCC BY 4.0arXiv

Applications of C*-Entropy to Representation Growth for Discrete Groups

  • Connor MacMahon
Open at sourcePDFDOICite

Abstract

The topological $1$-bounded entropy htop(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 SLn(Z) admits subexponential representation growth is recorded.

Related

  1. Representation stability for compact and discrete quantum groups
    Michael Brannan, Junichiro Matsuda, Erik Séguin
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Outer action of representation category of discrete quantum groups: a case study
    Debashish Goswami, Suchetana Samadder
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  3. Representation zeta functions of self-similar branched groups
    Laurent Bartholdi
    Groups, Geometry, and DynamicsPeer-reviewedLicence not statedFull text5 citedAlgebra & number theoryHAL
  4. Representation zeta functions of wreath products with finite groups
    Laurent Bartholdi, Pierre de La Harpe
    Groups, Geometry, and DynamicsPeer-reviewedLicence not statedFull text5 citedAlgebra & number theoryHAL
  5. Majorization, Entropy and Concentration Inequalities for Discrete α-Concave Random Variables
    Abdulmajeed Alqasem, Heshan Aravinda, Arnaud Marsiglietti
    arXivPreprintarXiv licenceFull textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{macmahon2026applications,
  title = {{Applications of $C^*$-Entropy to Representation Growth for Discrete Groups}},
  author = {Connor MacMahon},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21080},
  eprint = {2610.21080},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21080},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Applications of C^*-Entropy to Representation Growth for Discrete Groups
AU  - Connor MacMahon
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.21080
UR  - https://arxiv.org/abs/2610.21080
AB  - The topological $1$-bounded entropy h^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.
ER  -