{
  "abstract": "For every pair of integers $0\\leq k\\leq N,$ and and every subgroup of $D_N\\times\\mathbb{Z}_2$, we construct the nonnegative symmetric Grassmannian, which is the subspace of the nonnegative Grassmannian fixed under that group, where the dihedral part acts on columns (with a sign correction to keep nonnegativity) and the $\\mathbb{Z}_2$ factor exchanges a space with its orthocomplement (again, with a sign correction). This construction generalizes the earlier constructions of \\cite{Karpman2018,Fraser2020,Shevchenko2025}. We study the geometry of this space. Then, when $k$ is further restricted to the range $[2,N-2]$ we also define a symmetric amplituhedron. We analyze its basic properties and its conjectural BCFW decomposition. The ABJM and reflected Lagrangian amplituhedra are the special cases corresponding to the groups $\\{1\\}\\times\\mathbb{Z}_2,$ and the group generated by a reflection combined with the exchange,",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35604",
  "author_total": 1,
  "authors": [
    {
      "name": "Ran J. Tessler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvqfc3xpnvsps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35604",
  "fulltext_url": null,
  "id": "cvqfc3xpnvsps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35604",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7214775087",
  "pdf_url": "https://arxiv.org/pdf/2609.35604",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvqfc3xpnvsps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.35604",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35604"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Symmetric Amplituhedra I: Spinor Helicity",
  "title_text": "Symmetric Amplituhedra I: Spinor Helicity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/cvqfc3xpnvsps",
  "venue": "arXiv",
  "versions": []
}