Higher Gauss sums of modular categories
Higher Gauss sums of modular categories
复制标题
DOI：
10.1007/s00029-019-0499-2
复制
发表时间：
2018-12
期刊：
影响因子：
--
通讯作者：
S. Ng;Andrew Schopieray;Yilong Wang
中科院分区：
文献类型：
--
作者：
S. Ng;Andrew Schopieray;Yilong Wang
为预模范畴and 引入了第n 个高斯和和相关的第n 个中心电荷的定义。我们首先推导出模范畴的第二个高斯和的表达式，对于任何整数素数到 T 矩阵的阶，根据第一高斯和、全局维数、扭曲及其伽罗瓦共轭。因此，我们证明，较高的高斯和红数和相关的中心电荷是单位根。特别是，如果是球形融合类别的 Drinfeld 中心，则这些较高的中心电荷为 1。我们获得了用于去等变化和适当的预模和模类别的局部模块构造的更高高斯和的另一个表达式。然后应用这些表达式来证明伪酉模范畴的较高中心电荷的维特不变性。
The definitions of thenthGauss sumand the associatednthcentral chargeare introduced for premodular categoriesand. We first derive an expression of thenth Gauss sum of a modular category, for any integerncoprime to the order of the T-matrix of, in terms of the first Gauss sum, the global dimension, the twist and their Galois conjugates. As a consequence, we show for thesen, the higher Gauss sums ared-numbers and the associated central charges are roots of unity. In particular, ifis the Drinfeld center of a spherical fusion category, then these higher central charges are 1. We obtain another expression of higher Gauss sums for de-equivariantization and local module constructions of appropriate premodular and modular categories. These expressions are then applied to prove the Witt invariance of higher central charges for pseudounitary modular categories.