论文标题
拓扑量子场理论的上三角矩阵的虚拟类别形式类别
Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories
论文作者
论文摘要
在本文中，我们使用由González-Prieto，Logares，Muñoz和Newstead开发的几何技术来研究$ G $ - 代表的各种表面组$ \ Mathfrak {x} _g（x} _g（σ_g）$ g $ g $ g $ for $ g $ for $ g $ for $ g $ for $ g $是上层三角形的固定型固定等级的$ g $。明确地，我们在$ g $呈现品种的Grothendieck戒指中计算虚拟类别的虚拟类别，以及$ G $ - $ G $的模量空间，用于$ g $的表面组是复杂的上层三角矩阵等级$ 2 $，$ 3 $，$ 3 $，以及$ 4 $ $ 4 $，通过构建额外量子量子学字段。此外，我们表明，在上三角矩阵的情况下，字符图从$ g $ epressentations到$ g $ - 特定品种的模量空间不是同构。
In this paper, we use a geometric technique developed by González-Prieto, Logares, Muñoz, and Newstead to study the $G$-representation variety of surface groups $\mathfrak{X}_G(Σ_g)$ of arbitrary genus for $G$ being the group of upper triangular matrices of fixed rank. Explicitly, we compute the virtual classes in the Grothendieck ring of varieties of the $G$-representation variety and the moduli space of $G$-representations of surface groups for $G$ being the group of complex upper triangular matrices of rank $2$, $3$, and $4$ via constructing a topological quantum field theory. Furthermore, we show that in the case of upper triangular matrices the character map from the moduli space of $G$-representations to the $G$-character variety is not an isomorphism.
