{
  "abstract": "Spin space groups provide the natural symmetry framework for magnetic crystals with weak spin-orbit coupling, but extracting their physical consequences requires a general theory of irreducible representations. The central difficulty is that spin space groups are represented projectively: their factor systems can render lattice translations noncommuting, induce nonsymmorphic actions in momentum space, and modify the projective structure of little cogroups. These effects lie beyond conventional space-group and double-group representation theory. Here, using Mackey's theory of group extensions, we develop a unified constructive framework for all collinear, coplanar, and noncoplanar spin space groups, including antiunitary symmetries and general factor systems. A central technical result is a canonical decomposition of the relevant factor system $ν$ into a translational factor $σ$, a mixed factor $γ$ coupling translations to point-group operations, and a point-group factor $α$. This decomposition makes transparent how ordinary representation theory is modified: $σ$ determines the projective translation algebra and the appropriate Brillouin zone, $γ$ controls the momentum-space group action and can make it nonsymmorphic, and $α$ contributes to the factor systems of little cogroups. On this basis, we construct all projective irreducible corepresentations by induction over momentum-space orbits. The framework identifies which nonsymmorphic momentum-space symmetries can be realized by spin space groups and reveals Brillouin spaces that are compact flat manifolds rather than tori, symmetry-enforced Zak phases, reconstructed high-symmetry momenta and band degeneracies, and new types of quasiparticles. Our results establish the representation-theoretic foundation for systematic studies of weak-spin-orbit-coupled magnetic materials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21289",
  "author_total": 3,
  "authors": [
    {
      "name": "Zheng Zhang"
    },
    {
      "name": "Peiyuan Wang"
    },
    {
      "name": "Y. X. Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/708244f5525z7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21289",
  "fulltext_url": null,
  "id": "708244f5525z7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21289",
  "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",
      "cond-mat.mes-hall"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.21289",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/708244f5525z7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.21289",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21289"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Projective representation theory of spin space groups",
  "title_text": "Projective representation theory of spin space groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:03Z",
  "url": "https://research.draconitic.com/paper/708244f5525z7",
  "venue": "arXiv",
  "versions": []
}