发表机构
Birla Institute of Technology and Science, Pilani; Indian Institute of Science Education and Research, Mohali（比拉理工学院皮拉尼分校; 印度科学教育与研究学院莫哈利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出了花环积$G\wr \tilde{S}_n$的不可约自旋特征值的递归计算公式，并推广了0-1边界序列至移位Young图以简化实现。
AI 中文摘要
经典的Murnaghan-Nakayama规则是计算对称群$S_n$的复不可约特征值的递归公式。Alun Morris证明了用于计算$\tilde{S}_n$的不可约自旋特征值的递归公式，其中$\tilde{S}_n$是$S_n$的Schur覆盖之一，定义为$\tilde{S}_n:=\langle t_1,t_2,\cdots,t_{n-1},z\\ |\\ z^2=1,\\ t_i^2=z,\\ (t_it_{i+1})^3=z, \\ t_it_j=zt_jt_i\\ \text{if}\\ |i-j|>1\rangle$。J. Stembridge证明了用于计算花环积$G\wr S_n$（其中$G$是有限群）的复不可约特征值的递归公式。在本文中，我们陈述并证明了用于计算花环积$G\wr \tilde{S}_n$的不可约自旋特征值的递归公式。为了方便实现这些递归公式，我们将Young图的0-1边界序列的概念推广到移位Young图。
英文摘要
The classical Murnaghan-Nakayama rule is a recursive formula for computing the values of complex irreducible characters of the symmetric group $S_n$. Alun Morris proved a recursive formula for evaluating the values of irreducible spin characters of $\widetilde{S}_n$, where $\widetilde{S}_n$ is one of the Schur covers of $S_n$ defined by $\widetilde{S}_n:=\langle t_1,t_2,\cdots,t_{n-1},z\ |\ z^2=1,\ t_i^2=z,\ (t_it_{i+1})^3=z, \ t_it_j=zt_jt_i\ \text{if}\ |i-j|>1\rangle$. A recursive formula for evaluating the values of complex irreducible characters of the wreath product $G\wr S_n$, where $G$ is a finite group, was proved by J. Stembridge. In this article, we state and prove a recursive formula to compute the values of the irreducible spin characters of the wreath product $G\wr \widetilde{S}_n$. For the convenience of implementing these recursive formulas, we extend the notion of 0-1 boundary sequence of a Young diagram to shifted Young diagrams.
