Cluster structures on braid varieties
We show the existence of cluster $\mathcal {A} $-structures and cluster Poisson structures
on any braid variety, for any simple Lie group. The construction is achieved via weave …
on any braid variety, for any simple Lie group. The construction is achieved via weave …
[PDF][PDF] Braid variety cluster structures, II: general type
P Galashin, T Lam, M Sherman-Bennett - arXiv preprint arXiv:2301.07268, 2023 - arxiv.org
arXiv:2301.07268v2 [math.AG] 7 Feb 2023 Page 1 BRAID VARIETY CLUSTER STRUCTURES,
II: GENERAL TYPE PAVEL GALASHIN, THOMAS LAM, AND MELISSA SHERMAN-BENNETT …
II: GENERAL TYPE PAVEL GALASHIN, THOMAS LAM, AND MELISSA SHERMAN-BENNETT …
Positroid links and braid varieties
We study braid varieties and their relation to open positroid varieties. We discuss four
different types of braids associated to open positroid strata and show that their associated …
different types of braids associated to open positroid strata and show that their associated …
Plabic links, quivers, and skein relations
P Galashin, T Lam - arXiv preprint arXiv:2208.01175, 2022 - arxiv.org
We study relations between cluster algebra invariants and link invariants. First, we show that
several constructions of positroid links (permutation links, Richardson links, grid diagram …
several constructions of positroid links (permutation links, Richardson links, grid diagram …
Positive microlocal holonomies are globally regular
R Casals, W Li - arXiv preprint arXiv:2409.07435, 2024 - arxiv.org
We establish a geometric criterion for local microlocal holonomies to be globally regular on
the moduli space of Lagrangian fillings. This local-to-global regularity result holds for …
the moduli space of Lagrangian fillings. This local-to-global regularity result holds for …
Algebra and geometry of link homology: Lecture notes from the IHES 2021 Summer School
These notes cover the lectures of the first named author at 2021 IHES Summer School on
“Enumerative Geometry, Physics and Representation Theory” with additional details and …
“Enumerative Geometry, Physics and Representation Theory” with additional details and …
Analogs of the dual canonical bases for cluster algebras from Lie theory
F Qin - arXiv preprint arXiv:2407.02480, 2024 - arxiv.org
For almost all the known (quantum) cluster algebras from Lie theory, we construct the
common triangular bases. These bases provide analogs of the dual canonical bases which …
common triangular bases. These bases provide analogs of the dual canonical bases which …
On Leclerc's conjectural cluster structures for open Richardson varieties
In 2016, Leclerc constructed conjectural cluster structures on open Richardson varieties
using representations of preprojective algebras. A variant with more explicit seeds was …
using representations of preprojective algebras. A variant with more explicit seeds was …
Richardson varieties, projected Richardson varieties and positroid varieties
DE Speyer - arXiv preprint arXiv:2303.04831, 2023 - arxiv.org
This is a survey article on Richardson varieties and their combinatorics. A Richardson
variety is the intersection, inside the flag manifold GL_n/B_+, of a Schubert cell (B_-u …
variety is the intersection, inside the flag manifold GL_n/B_+, of a Schubert cell (B_-u …
Applications of the freezing operators on cluster algebras
F Qin - arXiv preprint arXiv:2407.03186, 2024 - arxiv.org
We apply freezing operators to relate different (quantum) upper cluster algebras. We prove
that these operators send localized (quantum) cluster monomials to localized (quantum) …
that these operators send localized (quantum) cluster monomials to localized (quantum) …