{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26506",
  "author_total": 2,
  "authors": [
    {
      "name": "Adrien Boyer"
    },
    {
      "name": "Thang Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55t07z78w8q2c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26506",
  "fulltext_url": null,
  "id": "55t07z78w8q2c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26506",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7222993967",
  "pdf_url": "https://arxiv.org/pdf/2610.26506",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55t07z78w8q2c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26506",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26506"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Property RD and boundary representations]{Property RD for $\\widetilde A_2$ groups\\\\and boundary representations",
  "title_text": "Property RD and boundary representations]{Property RD for Ã_2 groups\\\\and boundary representations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/55t07z78w8q2c",
  "venue": "arXiv",
  "versions": []
}