标题： 关于与仿射李代数相关的胶带张量范畴的单位性和模性 显示英文标题

标题： On the unitarity and modularity of ribbon tensor categories associated with affine Lie algebras

摘要： 我们研究从简单仿射李代数导出的扭带张量范畴的幺正性和模ularity，通过它们相关的量子群。 基于数值计算，并假设两个猜想，我们提供了对于$q$的哪些值这些扭带张量范畴是（伪）幺正的，以及对于$q$的哪些值它们是模的完整图景。 我们将结果与文献中出现的广泛严格结果进行比较，发现完全一致。 对于文献中未出现的情况，我们完善了这一图景。 显示英文摘要

摘要： We study the unitarity and modularity of ribbon tensor categories derived from simple affine Lie algebras, via their associated quantum groups. Based on numerical calculations, and assuming two conjectures, we provide the complete picture for which values of $q$ these ribbon tensor categories are (pseudo-)unitary and for which values of $q$ they are modular. We compare our results with the extensive rigorous results appearing in the literature, finding complete agreement. For the cases that do not appear in the literature, we complete the picture.