From amplituhedra to flagtopes

@misc{barkley2026from,
  title = {{From amplituhedra to flagtopes}},
  author = {Grant T. Barkley and Steven N. Karp and Kaitao Xie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37017},
  eprint = {2610.37017},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37017},
}

TY  - UNPB
TI  - From amplituhedra to flagtopes
AU  - Grant T. Barkley
AU  - Steven N. Karp
AU  - Kaitao Xie
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37017
UR  - https://arxiv.org/abs/2610.37017
AB  - The amplituhedron was introduced by Arkani-Hamed and Trnka (2014) to geometrically encode scattering amplitudes in high-energy physics. It can be viewed as the generalization of a cyclic polytope into the Grassmannian, and is defined to be the projection of the totally nonnegative part of one Grassmannian with respect to a totally negative element of a second Grassmannian. We construct a Lie-theoretic generalization of amplituhedra called 'flag amplituhedra', by replacing the pair of Grassmannians in the definition with an arbitrary pair of partial flag varieties for a reductive group G. We study in detail an example of a flag amplituhedron which is not a Grassmannian amplituhedron; it is a curved hexagon in ℙ^1× ℙ^1.
ER  -