Lefschetz invariants and Young characters for representations of the hyperoctahedral groups
Lefschetz invariants and Young characters for representations of the hyperoctahedral groups
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用于表示超八面体群的 Lefschetz 不变量和 Young 字符
DOI：
10.1016/j.jalgebra.2018.07.001
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
and T. Yoshida
中科院分区：
文献类型：
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作者：
F. Oda;Y. Takegahara;and T. Yoshida
超八面体群 B n 的虚拟 C 字符的环 R (B n) 具有两个由排列字符组成的 Z 基，与它们的每个基相关联的环结构定义了部分 Burnside 环，其中 R (B n) 是其同态图像。特别地，B n 的杨格子概念源于 B n 子群的某个集合 U n ，L. Geissinger 和 D. Kinch 提出的由杨格子组成的 R (B n) 的 Z 基 [7] 迫使 R (B n) 同构于部分 Burnside 环 Ω (B n, U n)。 B n 的线性 C 特征通过简化的 Lefschetz 不变量进行分析，该不变量表征了 Ω (B n, U n) 的单位群。抛物线Burnside环PB(Bn)是Ω(Bn,Un)的子环，PB(Bn)的单位群与四群同构。偶符号置换群 D n 的抛物线 Burnside 环的单位群也同构于四群。
The ring R (B n) of virtual C-characters of the hyperoctahedral group B n has two Z-bases consisting of permutation characters, and the ring structure associated with each basis of them defines a partial Burnside ring of which R (B n) is a homomorphic image. In particular, the concept of Young characters of B n arises from a certain set U n of subgroups of B n, and the Z-basis of R (B n) consisting of Young characters, which is presented by L. Geissinger and D. Kinch [7], forces R (B n) to be isomorphic to a partial Burnside ring Ω (B n, U n). The linear C-characters of B n are analyzed with reduced Lefschetz invariants which characterize the unit group of Ω (B n, U n). The parabolic Burnside ring PB (B n) is a subring of Ω (B n, U n), and the unit group of PB (B n) is isomorphic to the four group. The unit group of the parabolic Burnside ring of the even-signed permutation group D n is also isomorphic to the four group.