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Hecke categories, idempotents, and commuting stacks
Eugene Gorsky, Andrei Neguţ
We formulate a connection between a topological and a geometric category. The former is the idempotent completion of the (horizontal) trace of the affine Hecke category, while the…
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…
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…
Generic curves and non-coprime Catalans
Eugene Gorsky, Mikhail Mazin, Alexei Oblomkov
We compute the Poincaré polynomials of the compactified Jacobians for plane curve singularities with Puiseaux exponents , and relate them to the combinatorics of $q,…
Splicing positroid varieties
Eugene Gorsky, Tonie Scroggin
We construct an explicit isomorphism between an open subset in the open positroid variety in the Grassmannian and the product of two open posi…
Tautological classes and symmetry in Khovanov-Rozansky homology
Eugene Gorsky, Matthew Hogancamp, Anton Mellit
We define a new family of commuting operators in Khovanov-Rozansky link homology, similar to the action of tautological classes in cohomology of character varieties. We prove…