Unbounded ${\mathfrak{s}\mathfrak{l}}_3$-laminations around punctures

We continue to study the unbounded ${\mathfrak{s}\mathfrak{l}}_3$-laminations [IK22], with a focus on their structures at punctures. A key ingredient is their relation to the root data of ${\mathfrak{s}\mathfrak{l}}_3$. After giving a classification of signed ${\mathfrak{s}\mathfrak{l}}_3$-webs around a puncture, we describe the tropicalization of the Goncharov–Shen’s Weyl group action in detail. We also clarify the relationship with several other approaches by Shen–Sun–Weng [SSW23] and Fraser–Pylyavskyy [FP21]. Finally, we discuss a formulation of unbounded $\mathfrak{g}$-laminations for a general semisimple Lie algebra $\mathfrak{g}$ in brief.