ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2018
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| _version_ | 1866914686372413440 |
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| author | Bazier-Matte, Véronique Chapelier-Laget, Nathan Douville, Guillaume Mousavand, Kaveh Thomas, Hugh Yıldırım, Emine |
| author_facet | Bazier-Matte, Véronique Chapelier-Laget, Nathan Douville, Guillaume Mousavand, Kaveh Thomas, Hugh Yıldırım, Emine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_09986 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras Bazier-Matte, Véronique Chapelier-Laget, Nathan Douville, Guillaume Mousavand, Kaveh Thomas, Hugh Yıldırım, Emine Representation Theory Combinatorics 13F60, 16G20 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. |
| title | ABHY Associahedra and Newton polytopes of $F$-polynomials for finite type cluster algebras |
| topic | Representation Theory Combinatorics 13F60, 16G20 |
| url | https://arxiv.org/abs/1808.09986 |