33 citations · 65 across the 22 of their papers we have counts for
25 papers
Torus actions on compactified braid varieties and polytopality of subword complexes
Lara Bossinger, Mikhail Gorsky, José Simental
Every cluster variety admits an action of its cluster dilation group. We prove that, in the case of braid varieties for simple Lie groups, this action always extends to a regular a…
Mysterious points in keys but not trees
Scott Neville, José Simental
The deep locus of a cluster variety is defined to be the set of its points that do not belong to any cluster torus. We show that, if the cluster variety has a seed whose mutable pa…
Smooth correspondences between quiver varieties
Nicolle González, Eugene Gorsky, José Simental
We introduce a new class of smooth correspondences between Nakajima quiver varieties called split parabolic quiver varieties, and study their properties. We use these correspondenc…
Bruhat intervals that are large hypercubes
Jordan Ellenberg, Nicolas Libedinsky, David Plaza +2
We study the question of finding big Bruhat intervals that are poset hypercubes in the symmetric group . Using permutations suggested by AlphaEvolve (an evolutionary coding ag…
Cluster tori over , hexagonal moves on triangulations, and minimal coverings of cluster manifolds
Daniel Pérez Melesio, José Simental
We study cluster algebras over . By the Laurent phenomenon there is a map from the set of seeds of the cluster algebra to the corresponding cluster variety. We show t…
Comparing cluster algebras on braid varieties
Roger Casals, Pavel Galashin, Mikhail Gorsky +3
Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, posi…
Splicing braid varieties
Eugene Gorsky, Soyeon Kim, Tonie Scroggin +1
For a positive braid , we consider the braid variety . We define a family of open sets in , where is a permut…
Splicing skew shaped positroids
Eugene Gorsky, Soyeon Kim, Tonie Scroggin +1
Skew shaped positroids (or skew shaped positroid varieties) are certain Richardson varieties in the flag variety that admit a realization as explicit subvarieties of the Grassmanni…
The elliptic Hall algebra and the double Dyck path algebra
Nicolle Gonzalez, Eugene Gorsky, Jose Simental
We show that the positive half of the elliptic Hall algebra is embedded as a natural spherical subalgebra inside the double Dyck path algebra $\mathbb{B}_{q…
Cluster deep loci and mirror symmetry
Marco Castronovo, Mikhail Gorsky, José Simental +1
Affine cluster varieties are covered up to codimension 2 by open algebraic tori. We put forth a general conjecture (based on earlier conversation between Vivek Shende and the last…
Calibrated representations of the double Dyck path algebra
Nicolle González, Eugene Gorsky, José Simental
The double Dyck path algebra and its polynomial representation first arose as a key figure in the proof of the celebrated Shuffle Theorem of Carlsson and Mellit.…
Cluster algebras in Lie and Knot theory
Mikhail Gorsky, José Simental
This is a survey article on some connections between cluster algebras and link invariants, written for the Notices of the AMS.
Higher rank -Catalan polynomials, affine Springer fibers, and a finite Rational Shuffle Theorem
Nicolle González, José Simental, Monica Vazirani
We introduce the higher rank -Catalan polynomials and prove they equal truncations of the Hikita polynomial to a finite number of variables. Using affine compositions and a…
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…
Algebra and geometry of link homology
Eugene Gorsky, Oscar Kivinen, José Simental
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 referen…
Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions
Chris Bowman, Emily Norton, José Simental
We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these tw…
An elementary approach to the homological properties of constant-rank operators
Adolfo Arroyo-Rabasa, José Simental
We give a simple and constructive extension of Raiţă's result that every constant-rank operator possesses an exact potential and an exact annihilator. Our construction is completel…
Positroid Links and Braid varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +1
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 associate…
Algebraic Weaves and Braid Varieties
Roger Casals, Eugene Gorsky, Mikhail Gorsky +1
In this manuscript we study braid varieties, a class of affine algebraic varieties associated to positive braids. Several geometric constructions are presented, including certain t…
From representations of the rational Cherednik algebra to parabolic Hilbert schemes via the Dunkl-Opdam subalgebra
Eugene Gorsky, José Simental, Monica Vazirani
In this note we explicitly construct an action of the rational Cherednik algebra corresponding to the permutation representation of on the $\mat…
Representations with minimal support for quantized Gieseker varieties
Pavel Etingof, Vasily Krylov, Ivan Losev +1
We study the minimally supported representations of quantizations of Gieseker moduli spaces. We relate them to -equivariant D-modules on the nilpotent cone of…
Harish-Chandra bimodules for type A rational Cherednik algebras
José Simental
We study Harish-Chandra bimodules for the rational Cherednik algebra associated to the symmetric group . In particular, we show that for any parameter , th…
Characteristic-free bases and BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras
C. Bowman, E. Norton, J. Simental
We construct characteristic-free bases and BGG resolutions of unitary simple modules of quiver Hecke algebras and Cherednik algebras. We hence solve and vastly generalise Berkesch-…
Harish-Chandra bimodules over rational Cherednik algebras
José Simental
We study Harish-Chandra bimodules over the rational Cherednik algebra associated to a complex reflection group with parameter . Our results allow us to partially…