{
  "abstract": "We construct first-order ladder operators for spin-$\\frac{1}{2}$ Dirac fields and transverse, $γ$-traceless spin-$\\frac{3}{2}$ Rarita--Schwinger fields on maximally symmetric spaces using non-isometric closed conformal Killing vectors. For both spins, we find three distinct operators: two of them, $\\mathcal{D}$ and $\\mathcal{D}^{s}$, shift the conformal label as $Δ\\to Δ\\pm 1$, while a third operator, $\\widetilde{\\mathcal{D}}$, reverses the sign of the Dirac eigenvalue at fixed $Δ$. The latter exists in arbitrary dimensions and reduces to the standard infinitesimal conformal transformation of a primary spinor when acting on massless spin-$\\frac{1}{2}$ fields. On $S^N$, the ladder operators relate neighboring fermionic harmonics and generate the spinor tower from Killing-spinor seeds. In Lorentzian signature, we study their action on de Sitter mode spaces. In $dS_4$, the spin-$\\frac{3}{2}$ ladders connect the zero-Dirac-mass sector with the fermionic gauge points $M=\\pm i/\\ell$, while $\\widetilde{\\mathcal{D}}$ extends to arbitrary mass the conformal-like transformation previously identified for the gauge field. We explicitly present the spin-$\\frac{1}{2}$ and spin-$\\frac{3}{2}$ fermionic harmonics on spheres as well as the de Sitter mode solutions. Finally, we derive the Casimir operators on $S^3$, $dS_3$, and $dS_4$ corresponding to SO(4), SO(3,1) and SO(4,1), and relate their eigenvalues for UIRs to the allowed masses in the fermionic field equations. These results provide a unified geometric framework relating conformal Killing geometry, fermionic Dirac-type spectra, and the representation theory of maximally symmetric spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12088",
  "author_total": 3,
  "authors": [
    {
      "name": "Facundo L. Cruz"
    },
    {
      "name": "Matias N. Sempé"
    },
    {
      "name": "Guillermo A. Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bp59ejqz8m389.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12088",
  "fulltext_url": null,
  "id": "bp59ejqz8m389",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12088",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7213026393",
  "pdf_url": "https://arxiv.org/pdf/2609.12088",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bp59ejqz8m389.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12088",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12088"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Ladder Operators and Fermionic Tensor Fields on Maximally Symmetric Spaces",
  "title_text": "Ladder Operators and Fermionic Tensor Fields on Maximally Symmetric Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:07Z",
  "url": "https://research.draconitic.com/paper/bp59ejqz8m389",
  "venue": "arXiv",
  "versions": []
}