32 citations · 125 across the 13 of their papers we have counts for
13 papers
The Chromatic Lagrangian: Wavefunctions and Open Gromov-Witten Conjectures
Gus Schrader, Linhui Shen, Eric Zaslow
Inside a symplectic leaf of the cluster Poisson variety of Borel-decorated local systems on a punctured surface is an isotropic subvariety we will call the chromatic Lagran…
Cluster Nature of Quantum Groups
Linhui Shen
We present a rigid cluster model to realize the quantum group for of type ADE. That is, we prove that there is a natural Hopf algebra isomo…
Cluster structures on braid varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +3
We show the existence of cluster -structures and cluster Poisson structures on any braid variety, for any simple Lie group. The construction is achieved via weave calc…
for cluster algebras from moduli spaces of -local systems
Tsukasa Ishibashi, Hironori Oya, Linhui Shen
For a finite-dimensional simple Lie algebra admitting a non-trivial minuscule representation and a connected marked surface with at least two marked points and n…
Augmentations, Fillings, and Clusters
Honghao Gao, Linhui Shen, Daping Weng
We investigate positive braid Legendrian links via a Floer-theoretic approach and prove that their augmentation varieties are cluster K2 (aka. A-) varieties. Using the exact Lagran…
Duals of semisimple Poisson-Lie groups and cluster theory of moduli spaces of G-local systems
Linhui Shen
We study the dual of a standard semisimple Poisson-Lie group from a perspective of cluster theory. We show that the coordinate ring $\mathcal{O}({\rm G}^\a…
Quantum geometry of moduli spaces of local systems and representation theory
Alexander Goncharov, Linhui Shen
Let G be a split semi-simple adjoint group, and S a colored decorated surface, given by an oriented surface with punctures, special boundary points, and a specified collection of b…
Cluster Structures on Double Bott-Samelson Cells
Linhui Shen, Daping Weng
Let be a symmetrizable generalized Cartan matrix. We introduce four different versions of double Bott-Samelson cells for every pair of positive braids in the generalized braid…
Cyclic Sieving and Cluster Duality of Grassmannian
Linhui Shen, Daping Weng
We introduce a decorated configuration space with a potential function . We prove the cluster duality conjecture of Fock-Goncharov…
Donaldson-Thomas trasnsformations of moduli spaces of G-local systems
Alexander Goncharov, Linhui Shen
Kontsevich and Soibelman defined Donaldson-Thomas invariants of a 3d Calabi-Yau category equipped with a stability condition. Any cluster variety gives rise to a family of such cat…
Tensor invariants, Saturation problems, and Dynkin automorphisms
Jiuzu Hong, Linhui Shen
Let G be a connected almost simple algebraic group with a Dynkin automorphism σ. Let G_σ be the connected almost simple algebraic group associated to G and σ. We prove that the dim…
Geometry of canonical bases and mirror symmetry
Alexander Goncharov, Linhui Shen
A decorated surface S is a surface with a finite set of special points on the boundary, considered modulo isotopy. Let G be a split reductive group. A pair (G, S) gives rise to a m…
Stasheff polytopes and the coordinate ring of the cluster X-variety of type A_n
Linhui Shen
We define Stasheff polytopes in the space of tropical points of cluster A-varieties. We study the supports of products of elements of canonical bases for cluster X-varieties. We pr…