对称群的广义迭代圈积与广义有根树对应
Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence
摘要：
考虑对称群的广义迭代圈积$S_{r_1}\wr \ldots \wr S_{r_k}$。给出了广义迭代圈积遍历的完整描述。我们还证明了在某些有根树上的广义迭代圈积的普通不可约表示的等价类与标号轨道之间的双射的存在性。我们找到了广义迭代圈积的这些标号的个数和不可约表示的次数的递推公式。最后，我们给出了快速傅里叶变换的粗略上界估计。
英文摘要：
Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
