ABHY Associahedra and Newton polytopes of F-polynomials for cluster algebras of simply laced finite type
Journal of the London Mathematical Society, vol.109, no.1, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 109 Issue: 1
- Publication Date: 2024
- Doi Number: 10.1112/jlms.12817
- Journal Name: Journal of the London Mathematical Society
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Galatasaray University Affiliated: Yes
Abstract
A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitably understood) can be applied to construct generalized associahedra of any simply laced Dynkin type. Unexpectedly, we also show that this same construction produces Newton polytopes for all the (Formula presented.) -polynomials of the corresponding cluster algebras. In addition, we show that the toric variety associated to the (Formula presented.) -vector fan has the property that its nef cone is simplicial.