Cluster combinatorics of $SL_k$ skein algebras of punctured surfaces

Abstract: By work of several authors, the space of decorated $G$-local systems on a bordered marked surface is a cluster variety. When $G$ is $SL_2$, the associated cluster algebras are the cluster algebras from surfaces. We will present algebraic and combinatorial results and conjectures probing this family of cluster algebras when $G = SL_k$, in the spirit of previous work of Fomin-Shapiro-Thurston, Fomin-Pylyavskyy, and Goncharov-Shen. The main ingredients generalize tagged arcs and tagged triangulations from the $SL_2$ case. Joint with Pavlo Pylyavskyy.

mathematical physicscommutative algebraalgebraic geometrycombinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Online Cluster Algebra Seminar (OCAS)