{
  "abstract": "Let $H$ be a closed subgroup of a compact connected Lie group $G$ such that $G/H$ is simply connected, the action of $G$ on $G/H$ is almost effective, and $G/H$ is a strongly isotropy irreducible space. The smallest positive eigenvalue of the Laplace-Beltrami operator $Δ$ associated to the standard metric on $G/H$ was recently computed. In this article we obtain a second non-zero eigenvalue of $Δ$. As a consequence, we prove that all eigenspaces of the Laplacian are irreducible as $G$-modules if and only if $(G,H)$ is a compact symmetric pair of real rank one, or $(G,H)$ is equal to $(\\operatorname{G}_2,\\operatorname{SU}(3))$ or $(\\operatorname{Spin}(7),\\operatorname{G}_2)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15113",
  "author_total": 2,
  "authors": [
    {
      "name": "Emilio A. Lauret"
    },
    {
      "name": "Fiorela Rossi Bertone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rwwgvv9hqasv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15113",
  "fulltext_url": null,
  "id": "8rwwgvv9hqasv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15113",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221755766",
  "pdf_url": "https://arxiv.org/pdf/2610.15113",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rwwgvv9hqasv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15113",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15113"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Strongly isotropy irreducible spaces whose Laplacians have all their eigenspaces irreducible",
  "title_text": "Strongly isotropy irreducible spaces whose Laplacians have all their eigenspaces irreducible",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/8rwwgvv9hqasv",
  "venue": "arXiv",
  "versions": []
}