论文标题
G-Local Systems的模量空间的半神经泊松组和聚类理论的双重二元组
Duals of semisimple Poisson-Lie groups and cluster theory of moduli spaces of G-local systems
论文作者
论文摘要
我们从集群理论的角度研究了标准半玻璃poisson-lie组$ {\ rm g} $的双$ {\ rm g}^\ ast $。我们表明，坐标环$ \ MATHCAL {O}（{\ rm G}^\ ast）$可以自然地嵌入使用Weyl group Action的群集Poisson代数中。我们证明$ \ Mathcal {O}（{\ rm G}^\ ast）$允许自然基础，该基础具有正整数结构系数，并且满足了对编织组动作的不变性属性。我们继续研究Moduli空间$ \ MATHSCR {p} _ {{\ rm G}，\ Mathbb {s}} $的$ {\ rm g} $ - \ cite {gs3}中引入的本地系统，并证明了$ \ mathscr的均值环， \ mathbb {s}} $与其基础群集Poisson代数重合。
We study the dual ${\rm G}^\ast$ of a standard semisimple Poisson-Lie group ${\rm G}$ from a perspective of cluster theory. We show that the coordinate ring $\mathcal{O}({\rm G}^\ast)$ can be naturally embedded into a cluster Poisson algebra with a Weyl group action. We prove that $\mathcal{O}({\rm G}^\ast)$ admits a natural basis which has positive integer structure coefficients and satisfies an invariance property with respect to a braid group action. We continue the study of the moduli space $\mathscr{P}_{{\rm G},\mathbb{S}}$ of ${\rm G}$-local systems introduced in \cite{GS3}, and prove that the coordinate ring of $\mathscr{P}_{{\rm G}, \mathbb{S}}$ coincides with its underlying cluster Poisson algebra.
