标题： 球面融合范畴中旋转和辫子的特征值 显示英文标题

标题： Eigenvalues of rotations and braids in spherical fusion categories

摘要： 我们给出了半单球形张量范畴$\mathcal{C}$中广义旋转算子的特征值重数公式，这些公式以广义Frobenius-Schur指示器表示。特别是，这意味着融合范畴的所有旋转特征值集合都可以从融合规则和有限多张量幂上的旋转迹计算出来。 我们还通过琼斯的平面代数理论建立了具有特定融合环的融合范畴FS指示器的刚性性质。 如果$\mathcal{C}$还是辫的，这些公式可以得出大类辫在相关辫群表示中的特征值重数。 当$\mathcal{C}$是模的时，这使得可以根据$S$和$T$矩阵确定辫的特征值和重数。 显示英文摘要

摘要： We give formulae for the multiplicities of eigenvalues of generalized rotation operators in terms of generalized Frobenius-Schur indicators in a semisimple spherical tensor category $\mathcal{C}$. In particular, this implies that the entire collection of rotation eigenvalues for a fusion category can be computed from the fusion rules and the traces of rotation at finitely many tensor powers. We also establish a rigidity property for FS indicators of fusion categories with a given fusion ring via Jones's theory of planar algebras. If $\mathcal{C}$ is also braided, these formulae yield the multiplicities of eigenvalues for a large class of braids in the associated braid group representations. When $\mathcal{C}$ is modular, this allows one to determine the eigenvalues and multiplicities of braids in terms of just the $S$ and $T$ matrices.