论文标题
希尔伯特方案，维尔玛模块和双曲线几何的光谱函数，并应用于量子不变性
Hilbert schemes, Verma modules and spectral functions of hyperbolic geometry with application to quantum invariants
论文作者
论文摘要
在本文中，我们利用Ruelle-type光谱功能，并分析Virasoro代数的Verma模块，Boson-Fermion对应关系，分析扭转，Chern-Simons和$η$不变式，以及与交叉产品$ \ MathBB的hochsChild同源函数相关的生成函数。 \ Mathcal {a}^{\ otimes n} $（$ \ Mathcal {a} $是$ q $ -weyl algebra）。在分析了Chern-simons和$η$不变的狄拉克运算符之后，通过在非阳性部分曲率的本地对称歧管上使用不可约的$ su（n）$ - 平面连接，我们描述了Chern-Simons理论的指数动作。
In this article we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson-fermion correspondence, the analytic torsion, the Chern-Simons and $η$ invariants, as well as the generation function associated to dimensions of the Hochschild homology of the crossed product $\mathbb{C}[S_n]\ltimes \mathcal{A}^{\otimes n}$ ($\mathcal{A}$ is the $q$-Weyl algebra). After analysing the Chern-Simons and $η$ invariants of Dirac operators by using irreducible $SU(n)$-flat connections on locally symmetric manifolds of non-positive section curvature, we describe the exponential action for the Chern-Simons theory.
