论文标题
关于框架本地系统的部分阿belianization
On partial abelianization of framed local systems
论文作者
论文摘要
D.我们将此构造概括为$ \ mathrm {gl} _2（a）$的组的$ g $，其中$ a $是一个Unital Associative环，以及其某些子组。这取决于对与光谱网络和三角形相关的2度覆盖物的精确分析以及对路径提升规则的矩阵重新解释；在此过程中，我们提供了A.〜Berenstein和V.〜Retakh揭示的桂冠现象的另一个证据。部分Abelianization使我们能够为装饰的$ G $ - 本地系统和框后的$ G $ - 局部系统的模量空间进行参数化。对于$（a，σ）$ a Hermitian涉及$ \ mathbf {r} $ - 代数 - 组$ g = \ mathrm {sp} _2（a，σ）$是类型的古典遗产谎言组，我们能够识别和参数Maximal FraDameD odamal FraDameD odamal frailamed frailabeD $ g $ -local。
D.~Gaiotto, G.~W.~Moore and A.~Neitzke introduced spectral networks to understand the framed $G$-local systems over punctured surfaces for $G$ a split Lie group via a procedure called abelianization. We generalize this construction to groups $G$ of the form $\mathrm{GL}_2(A)$, where $A$ is a unital associative ring, and to some of its subgroups. This relies on a precise analysis of the degree 2 ramified coverings associated with spectral networks and triangulations and on a matrix reinterpretation of their path lifting rules; along the way we provide another proof of the Laurent phenomenon brought to light by A.~Berenstein and V.~Retakh. The partial abelianization enables us to gives parametrizations of the moduli spaces of decorated $G$-local systems and of framed $G$-local systems over punctured surfaces. For $(A, σ)$ a Hermitian involutive $\mathbf{R}$-algebra the group $G=\mathrm{Sp}_2(A, σ)$ is a classical Hermitian Lie group of tube type, and we are able to identify and parametrize the moduli space of maximal framed $G$-local systems.
