AI 中文总结
本文从带边张量范畴及其平衡辫子模范畴出发，构造带线缺陷三维流形的辫理论，证明量子对称对缺陷辫模的有限性，并在特定情形下建立与Z2等变辫理论的等价，进而构造Type AIII情形的C∨C DAHA模。
AI 中文摘要
我们从带边张量范畴及其平衡辫子模范畴的数据出发，为带有嵌入线缺陷的三维流形构造辫理论。我们聚焦于由量子对称对产生的线缺陷，并证明其缺陷辫模的有限性性质。作为应用，我们考虑$\mathbf{Z}_2$-等变辫理论，并在特定情形下建立其与缺陷辫理论的等价性，从而在Type AIII情形下给出$\mathrm{C}^\vee\mathrm{C}$ DAHA模族的一个辫理论构造。
英文摘要
We construct skein theory for 3-manifolds with embedded line defects, starting from the data of a ribbon tensor category and its balanced braided module category. We focus on line defects arising from quantum symmetric pairs, and prove finiteness properties for their defect skein modules. As an application, we consider $\mathbf{Z}_2$-equivariant skein theory and establish an equivalence with defect skein theory in certain settings, leading to a skein theoretical construction of a family of $\mathrm{C}^\vee\mathrm{C}$ DAHA-modules in the Type AIII case.
Comments32 pages. Comments welcome!
