3 papers
math.RT2024
Cluster structure on genus 2 spherical DAHA: seven-colored flower
Semeon Arthamonov, Leonid Chekhov, Philippe Di Francesco +4
We construct an embedding of the Arthamonov-Shakirov algebra of genus 2 knot operators into the quantized coordinate ring of the cluster Poisson variety of exceptional finite mutat…
math.GT2020
Fenchel--Nielsen coordinates and Goldman brackets
Leonid O. Chekhov
We explicitly show that the Poisson bracket on the set of shear coordinates introduced by V.V. Fock in 1997 induces the Fenchel--Nielsen bracket on the set of gluing parameters (le…
math.QA2020
Darboux coordinates for symplectic groupoid and cluster algebras
L. Chekhov, M. Shapiro
Using Fock--Goncharov higher Teichmüller space variables we derive Darboux coordinate representation for entries of general symplectic leaves of the groupoid of uppe…