Cluster Structures on Double Bott–Samelson Cells
نویسندگان
چکیده
Abstract Let $\mathsf {C}$ be a symmetrisable generalised Cartan matrix. We introduce four different versions of double Bott–Samelson cells for every pair positive braids in the braid group associated to . prove that decorated are smooth affine varieties, whose coordinate rings naturally isomorphic upper cluster algebras. explicitly describe Donaldson–Thomas transformations on and they transformations. As an application, we complete proof Fock–Goncharov duality conjecture these cases. discover periodicity phenomenon family cells. give (rather simple) geometric Zamolodchikov’s cases $\Delta \square \mathrm {A}_r$ When is type $\mathrm {A}$ , Shende–Treumann–Zaslow’s moduli spaces microlocal rank-1 constructible sheaves Legendrian links. By counting their $\mathbb {F}_q$ -points obtain rational functions link invariants.
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ژورنال
عنوان ژورنال: Forum of Mathematics, Sigma
سال: 2021
ISSN: ['2050-5094']
DOI: https://doi.org/10.1017/fms.2021.59