3 papers
math.CO2024
Punctured surfaces, quiver mutations, and quotients of Coxeter groups
Anna Felikson, Michael Shapiro, Pavel Tumarkin
In 2011, Barot and Marsh provided an explicit construction of presentation of a finite Weyl group by any quiver mutation-equivalent to an orientation of a Dynkin diagram with W…
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.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…