论文标题
$ g（d，1，n）$的傅立叶矩阵来自量子通用线性组
Fourier matrices for $G(d,1,n)$ from quantum general linear groups
论文作者
论文摘要
我们构建了与Spetsial Complex Reflection $ g（D，1，N）$的每个单位字符家族相关的模块化数据的分类。该类别的构建遵循傅立叶矩阵的分解，作为角色表的外部功能的Kronecker张量产品，该订单$ d $的循环型组$ s $。量子通用包络代数的代表，一般线性谎言lie代数$ \ mathfrak {gl} _m $，带有量子参数的均匀订单$ 2D $的均匀词，提供了矩阵$ \ big big big big big big bigwedge^m s $的分类解释。我们还证明了cuntz在脱离级别上的一些积极猜想。
We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G(d,1,n)$. The construction of the category follows the decomposition of the Fourier matrix as a Kronecker tensor product of exterior powers of the character table $S$ of the cyclic group of order $d$. The representation of the quantum universal enveloping algebra of the general linear Lie algebra $\mathfrak{gl}_m$, with quantum parameter an even root of unity of order $2d$, provides a categorical interpretation of the matrix $\bigwedge^m S$. We also prove some positivity conjectures of Cuntz at the decategorified level.
