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PreprintCC BY 4.0arXiv

Property RD and boundary representations]{Property RD for Ã2 groups\\and boundary representations

  • Adrien Boyer
  • Thang Nguyen
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Abstract

We develop a boundary representation approach to Rapid Decay property for groups acting on buildings of type Ã2. The central estimate combines a multiplicity argument on the product of Furstenberg boundary with the Riesz--Thorin theorem. For simply transitive actions on vertices, we also establish the polynomial bound conjectured by Ramagge, Robertson and Steger in the vector-radial case. The cubic degree of this bound is optimal. The method also uses multiplicity argument with the Riesz--Thorin theorem but on the single Furstenberg boundary.

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Cite

BibTeXRIS
BibTeX
@misc{boyer2026property,
  title = {{Property RD and boundary representations]Property RD for $\widetilde A_2$ groups\\and boundary representations}},
  author = {Adrien Boyer and Thang Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26506},
  eprint = {2610.26506},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26506},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Property RD and boundary representations]{Property RD for Ã_2 groups\\and boundary representations
AU  - Adrien Boyer
AU  - Thang Nguyen
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26506
UR  - https://arxiv.org/abs/2610.26506
AB  - We develop a boundary representation approach to Rapid Decay property for groups acting on buildings of type Ã_2. The central estimate combines a multiplicity argument on the product of Furstenberg boundary with the Riesz--Thorin theorem. For simply transitive actions on vertices, we also establish the polynomial bound conjectured by Ramagge, Robertson and Steger in the vector-radial case. The cubic degree of this bound is optimal. The method also uses multiplicity argument with the Riesz--Thorin theorem but on the single Furstenberg boundary.
ER  -