论文标题
装饰超级Teichmüller空间的矩阵公式
Matrix Formulae for Decorated Super Teichmüller Spaces
论文作者
论文摘要
对于带有标记点的边界表面上的弧线，我们使用SuperGroup $ \ Mathrm {osp}元素的产物将单位矩阵关联，该元素定义了平面$ \ Mathrm {osp}（osp}（1 | 2）（1 | 2）$ - 表面上的连接。我们表明，我们的ARC的矩阵公式在Penner-Zeitlin装饰的SuperTeichmüller空间中产生其超级$λ$长度。这概括了Fock-Goncharov和Musiker-Williams的矩阵公式。我们还证明，我们的矩阵公式与作者以前的作品中给出的组合公式一致。作为一个应用程序，我们在环方面使用矩阵公式来获得超级斐波那契数的新结果。
For an arc on a bordered surface with marked points, we associate a holonomy matrix using a product of elements of the supergroup $\mathrm{OSp}(1|2)$, which defines a flat $\mathrm{OSp}(1|2)$-connection on the surface. We show that our matrix formulas of an arc yields its super $λ$-length in Penner-Zeitlin's decorated super Teichmüller space. This generalizes the matrix formulas of Fock-Goncharov and Musiker-Williams. We also prove that our matrix formulas agree with the combinatorial formulas given in the authors' previous works. As an application, we use our matrix formula in the case of an annulus to obtain new results on super Fibonacci numbers.
