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Symmetric Amplituhedra I: Spinor Helicity

  • Ran J. Tessler
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Abstract

For every pair of integers 0≤ k≤ N, and and every subgroup of DN×ℤ2, 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 ℤ2 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}×ℤ2, and the group generated by a reflection combined with the exchange,

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Cite

BibTeXRIS
BibTeX
@misc{tessler2026symmetric,
  title = {{Symmetric Amplituhedra I: Spinor Helicity}},
  author = {Ran J. Tessler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35604},
  eprint = {2609.35604},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35604},
}
RIS
TY  - UNPB
TI  - Symmetric Amplituhedra I: Spinor Helicity
AU  - Ran J. Tessler
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35604
UR  - https://arxiv.org/abs/2609.35604
AB  - For every pair of integers 0≤ k≤ N, and and every subgroup of D_N×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 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}×ℤ_2, and the group generated by a reflection combined with the exchange,
ER  -