Cluster structures on braid varieties

Abstract: A braid variety is a certain affine algebraic variety associated with a simply-connected simple algebraic group G and a positive braid of the corresponding type. These varieties generalise open Richardson varieties and appear in the context of symplectic topology and in the study of link invariants such as HOMFLY-PT polynomials and Khovanov-Rozansky homology. In this talk, I will give a proof of the existence of cluster A-structures and cluster Poisson structures on any braid variety. I will sketch an explicit construction of cluster seeds involving the diagrammatic calculus of weaves and a tropicalization of Lustig's coordinates. These cluster algebras are local acyclic and equal their upper cluster algebras. The main result also proves the conjecture of B. Leclerc on the existence of cluster algebra structures on the coordinate rings of open Richardson varieties in simply laced types. The talk is based on joint work with Roger Casals, Eugene Gorsky, Ian Le, Linhui Shen, and José Simental.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: Meeting Link uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09

Meeting ID: 918 7552 8987 Password: LAGOON2022

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

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