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arXiv · 1808.09986

ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras

Véronique Bazier-Matte·Nathan Chapelier-Laget·Guillaume Douville·Kaveh Mousavand·Hugh Thomas·Emine Yıldırım
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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 $F$-polynomials of the corresponding cluster algebras. In addition, we show that the toric variety associated to the g-vector fan has the property that its nef cone is simplicial.

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Véronique Bazier-Matte, Nathan Chapelier-Laget, Guillaume Douville, Kaveh Mousavand, Hugh Thomas, Emine Yıldırım. 2021-10-19. ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras. https://doi.org/10.1112/jlms.12817

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