论文标题
无界的$ \ mathfrak {sl} _3 $ lAminations及其剪切坐标
Unbounded $\mathfrak{sl}_3$-laminations and their shear coordinates
论文作者
论文摘要
在理性无限的层压板上概括了Fock的工作，我们给出了群集品种的热带点$ \ Mathcal {X} _ {\ Mathfrak {\ Mathfrak {sl} _3，σ} $的几何模型$ \ mathfrak {sl} _3 $ -webs。我们将他们的热带簇坐标介绍为$ \ mathfrak {sl} _3 $ - 瑟斯顿的剪切坐标与任何理想的三角剖分相关的Analogue。作为模量空间中胶状形态的热带类似物，goncharov- shen的$ \ mathcal {p} _ {pgl_3，σ} $ - 我们描述了一个无绑定的$ \ mathfrak {sl rak} _3 $ - _3 $ lAMINISS pinnings via pinnings的几何粘合过程。我们还研究了与$ \ mathfrak {sl} _3 $ -Skein代数[IY23]的图形基础的关系，该基因构成了量子双重性图。
Generalizing the work of Fock--Goncharov on rational unbounded laminations, we give a geometric model of the tropical points of the cluster variety $\mathcal{X}_{\mathfrak{sl}_3,Σ}$, which we call unbounded $\mathfrak{sl}_3$-laminations, based on the Kuperberg's $\mathfrak{sl}_3$-webs. We introduce their tropical cluster coordinates as an $\mathfrak{sl}_3$-analogue of the Thurston's shear coordinates associated with any ideal triangulation. As a tropical analogue of gluing morphisms among the moduli spaces $\mathcal{P}_{PGL_3,Σ}$ of Goncharov--Shen, we describe a geometric gluing procedure of unbounded $\mathfrak{sl}_3$-laminations with pinnings via ``shearings''. We also investigate a relation to the graphical basis of the $\mathfrak{sl}_3$-skein algebra [IY23], which conjecturally leads to a quantum duality map.
