{
  "abstract": "Let $X=G/H$ be a real reductive symmetric space. We consider the support of the Plancherel measure for the regular representation of $G$ on $L^2(X)$, and its Fell topology. We first recall how the Plancherel formula for $X$ (known from work of Delorme and van den Ban--Schlicktrull, among others) yields a description of the support in terms of the discrete spectra of smaller symmetric spaces. We then point out that this description simplifies for a class of real symmetric spaces $X$ which we call well-tempered. These are the spaces whose tangent space at the identity coset admits a Cartan subspace whose centralizer in the Lie algebra of $G$ is abelian. Well-tempered spaces are tempered in the sense of Benoist and Kobayashi. Under mild assumptions on the disconnectedness of $G$, we give a description of the support of the Plancherel measure for well-tempered symmetric spaces in terms of characters of Cartan subgroups of $G$, and describe the Fell topology of the support. If $G$ is a complex group and $H$ a real form, then the support decomposes as a union of explicit quotients of relative continuous-parameter spaces by finite Weyl groups. As an application, we describe the $C^*$-algebra associated to the regular representation of $G$ on $L^2(X)$, and its $K$-theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32916",
  "author_total": 4,
  "authors": [
    {
      "name": "Alexandre Afgoustidis"
    },
    {
      "name": "Peter Hochs"
    },
    {
      "name": "Shintaro Nishikawa"
    },
    {
      "name": "Yanli Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/edn4fry5mvhss.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32916",
  "fulltext_url": null,
  "id": "edn4fry5mvhss",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32916",
  "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.OA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214733856",
  "pdf_url": "https://arxiv.org/pdf/2609.32916",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/edn4fry5mvhss.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32916",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32916"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Well-tempered symmetric spaces",
  "title_text": "Well-tempered symmetric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/edn4fry5mvhss",
  "venue": "arXiv",
  "versions": []
}