{
  "abstract": "Let $G$ be a reductive group over a number field $F$. We define $C^*_{\\rm aut}(G(\\mathbb A))$, the automorphic $C^*$-algebra of $G$, to be the $C^*$-algebraic image of the full automorphic representation of $G(\\mathbb A)$ on $L^2(G(F)\\backslash G(\\mathbb A))$. Using the Langlands spectral decomposition with respect to discrete Levi data, we construct an injective $*$-homomorphism \\[ C^*_{\\rm aut}(G(\\mathbb A)) \\longrightarrow \\bigoplus_{[M,σ]} K_{C_0(\\widehat{A_M})} \\left( \\operatorname{Ind}_P^G C_0(\\widehat{A_M},H_{M,σ}) \\right)^{W(G,M,σ)}, \\] where $[M,σ]$ ranges over the associate classes of discrete Levi data. When $G$ is $\\operatorname{GL}(n)$ or an inner form of it, we prove that this map is an isomorphism of $C^*$-algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35543",
  "author_total": 1,
  "authors": [
    {
      "name": "Jun Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vs1mwv2ftpm2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35543",
  "fulltext_url": null,
  "id": "1vs1mwv2ftpm2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35543",
  "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.NT"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214722867",
  "pdf_url": "https://arxiv.org/pdf/2609.35543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vs1mwv2ftpm2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Automorphic $C^*$-algebras of reductive groups",
  "title_text": "Automorphic C^*-algebras of reductive groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/1vs1mwv2ftpm2",
  "venue": "arXiv",
  "versions": []
}