Comparing cluster algebras on braid varieties
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918115712958464 |
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| author | Casals, Roger Galashin, Pavel Gorsky, Mikhail Shen, Linhui Sherman-Bennett, Melissa Simental, José |
| author_facet | Casals, Roger Galashin, Pavel Gorsky, Mikhail Shen, Linhui Sherman-Bennett, Melissa Simental, José |
| contents | Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, positroid varieties, open Bott-Samelson varieties, and Richardson varieties, among others. Recently, two cluster algebra structures were independently constructed in the coordinate rings of braid varieties: one using weaves and the other using Deodhar geometry. The main result of the article is that these two cluster algebras coincide. More generally, our comparative study matches the different concepts and results from each approach to the other, both on the combinatorial and algebraic geometric aspects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparing cluster algebras on braid varieties Casals, Roger Galashin, Pavel Gorsky, Mikhail Shen, Linhui Sherman-Bennett, Melissa Simental, José Algebraic Geometry Combinatorics Representation Theory Symplectic Geometry 13F60, 14M15, 05E99 Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, positroid varieties, open Bott-Samelson varieties, and Richardson varieties, among others. Recently, two cluster algebra structures were independently constructed in the coordinate rings of braid varieties: one using weaves and the other using Deodhar geometry. The main result of the article is that these two cluster algebras coincide. More generally, our comparative study matches the different concepts and results from each approach to the other, both on the combinatorial and algebraic geometric aspects. |
| title | Comparing cluster algebras on braid varieties |
| topic | Algebraic Geometry Combinatorics Representation Theory Symplectic Geometry 13F60, 14M15, 05E99 |
| url | https://arxiv.org/abs/2508.03816 |