{
  "abstract": "Let $π:G\\to \\mathcal{U}(L^{2}(G/P,ν))$ be the boundary representation of a non-compact connected semisimple Lie group $G$ with finite center on its Furstenberg-Poisson boundary $(G/P,ν)$. Let $Γ\\subset G$ be a lattice in $G$ (uniform or not). We show that for any \\emph{continuous} functions $φ,ψ,φ',ψ'$ on $G/P$, $$ \\lim_{n\\to\\infty}\\frac{1}{|Γ_{n}|}\\sum_{γ\\in Γ_{n}}\\frac{\\langleπ(γ)φ,ψ\\rangle\\overline{\\langleπ(γ)φ',ψ'\\rangle}}{Ξ^{2}(γ)}=\\langle φ,φ'\\rangle\\overline{\\langleψ,ψ'\\rangle}, $$ where $Γ_{n}$ is a ball in $Γ$ with radius $n$ relative to a natural length function and with center the identity element of $G$, and $Ξ$ is the restriction to $Γ$ of the Harish-Chandra function of $G$. As a corollary, we deduce that when the real rank of $G$ is one, then the analogous convergence holds for any $φ,ψ,φ',ψ'$ in $L^{2}(G/P,ν)$ if and only if the lattice $Γ$ is uniform.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04330",
  "author_total": 3,
  "authors": [
    {
      "name": "A. BENDIKOV"
    },
    {
      "name": "A. BOYER"
    },
    {
      "name": "CH. PITTET"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3zs11s4ftv8t0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04330",
  "fulltext_url": null,
  "id": "3zs11s4ftv8t0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04330",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7220716426",
  "pdf_url": "https://arxiv.org/pdf/2610.04330",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3zs11s4ftv8t0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04330",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04330"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Asymptotic Schur orthogonality for lattices",
  "title_text": "Asymptotic Schur orthogonality for lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/3zs11s4ftv8t0",
  "venue": "arXiv",
  "versions": []
}