Yang-Yang函数、Monodromy和Knot多项式
Yang-Yang functions, Monodromy and knot polynomials
摘要：
本文从一族Yang-Yang函数出发，导出了$\mathbb{Z}[t,t^{-1}]$ -模丛的结构.对于经典型复单李代数的基本表示，给出了明确的穿墙公式，并证明了$\mathbb{Z}[t,t^{-1}]$ -模丛的单值表示等价于由$U_{h}(g)$的泛R-矩阵诱导的辫群表示.我们证明了对称破缺变形和两个复参数的旋转在纤维上引起的两个变换是可交换的。
英文摘要：
We derive a structure of $\mathbb{Z}[t,t^{-1}]$-module bundle from a family of Yang-Yang functions. For the fundamental representation of the complex simple Lie algebra of classical type, we give explicit wall-crossing formula and prove that the monodromy representation of the $\mathbb{Z}[t,t^{-1}]$-module bundle is equivalent to the braid group representation induced by the universal R-matrices of $U_{h}(g)$. We show that two transformations induced on the fiber by the symmetry breaking deformation and respectively the rotation of two complex parameters commute with each other.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
