Dominance regions for affine cluster algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911297759608832 |
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| author | Reading, Nathan Rupel, Dylan Stella, Salvatore |
| author_facet | Reading, Nathan Rupel, Dylan Stella, Salvatore |
| contents | We determine dominance regions associated to cluster algebras of affine type. In the most interesting cases, the dominance region is a line segment, which we describe explicitly. Motivations for this work include a project to determine all pointed bases for cluster algebras of affine type and a separate project to determine all theta functions in the affine case. The proofs draw on known results from the doubled Cambrian fan and almost-positive roots models, as well as a new tool that we develop: a detailed description of neighboring seeds of affine type (seeds that are, in some sense, as close as possible to the boundary of the g-vector fan). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dominance regions for affine cluster algebras Reading, Nathan Rupel, Dylan Stella, Salvatore Representation Theory Combinatorics 13F60 We determine dominance regions associated to cluster algebras of affine type. In the most interesting cases, the dominance region is a line segment, which we describe explicitly. Motivations for this work include a project to determine all pointed bases for cluster algebras of affine type and a separate project to determine all theta functions in the affine case. The proofs draw on known results from the doubled Cambrian fan and almost-positive roots models, as well as a new tool that we develop: a detailed description of neighboring seeds of affine type (seeds that are, in some sense, as close as possible to the boundary of the g-vector fan). |
| title | Dominance regions for affine cluster algebras |
| topic | Representation Theory Combinatorics 13F60 |
| url | https://arxiv.org/abs/2512.02218 |