Property RD and boundary representations]{Property RD for $\widetilde A_2$ groups\\and boundary representations
Year: 2026
Type: preprint
Abstract: We develop a boundary representation approach to Rapid Decay property for groups acting on buildings of type $\widetilde A_2$. 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.
Source: arXiv (Cornell University)
Authors: Boyer, Adrien, Nguyen, Thang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7222993967