{
  "abstract": "Let $G$ be a compact connected Lie group and $K$ its connected Lie subgroup. Using the $K$-theoretic version of equivariant formality developed in [F2] which involves analysis of vector bundles over $G/K$, we find two characterizations of equivariant formality of the isotropy action of $K$ on $G/K$. The first one equates equivariant formality with a \"smoothness\" condition of the restriction map of the representation ring of $G$ to that of $K$. The second characterization asserts that equivariant formality amounts to the equivariant $K$-theoretic index pairing of two certain special $K$-theory classes being nontrivial in some sense. By applying these characterizations, we are able to give a representation theoretic criterion for equivariant formality of the isotropy action by a circle subgroup, as well as an invariant theory criterion for the case where $K$ is a torus of dimension one less than the rank of $G$, culminating in a complete classification of equivariant formality where $G$ is further assumed to be simple.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00448",
  "author_total": 1,
  "authors": [
    {
      "name": "Chi-Kwong Fok"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ayegrc58t37rf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00448",
  "fulltext_url": null,
  "id": "ayegrc58t37rf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00448",
  "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.AT"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7206201088",
  "pdf_url": "https://arxiv.org/pdf/2609.00448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ayegrc58t37rf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2609.00448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00448"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Equivariant formality and representation theory",
  "title_text": "Equivariant formality and representation theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/ayegrc58t37rf",
  "venue": "arXiv",
  "versions": []
}