Abstract We study crossed S-matrices for braided G-crossed categories and reduce their computation to a submatrix of the de-equivariantization. We study the more general case of a category containing the symmetric category Rep ( A , z ) with A a finite cyclic group and z ∈ A such that z 2 = 1 . We give two examples of such categories, which enable us to recover the Fourier matrix associated with the big family of unipotent characters of the dihedral groups with automorphism as well as the Fourier matrix of the big family of unipotent characters of the Ree group of type F 4 2 .

中文翻译：

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具有自同构的 Coxeter 群的交叉 S 矩阵和傅立叶矩阵

摘要 我们研究了编织 G 交叉类别的交叉 S 矩阵，并将它们的计算减少到去等变的子矩阵。我们研究包含对称类别 Rep ( A , z ) 的类别的更一般情况，其中 A 是有限循环群且 z ∈ A 使得 z 2 = 1 。我们给出了此类类别的两个例子，这使我们能够恢复与具有自同构的二面体群的单能特征大族相关的傅立叶矩阵以及类型 F 的 Ree 群的单能特征大族的傅立叶矩阵4 2 .