We relate the character theory of the symmetric groups ${\mathbb{S}}_{2n}$ and ${\mathbb{S}}_{2n+1}$ with that of the hyperoctahedral group ${\mathbb{B}}_n={(\mathbb{Z}/2)}^n⋊{\mathbb{S}}_n$, as part of the expectation that the character theory of reductive groups with diagram automorphism and their Weyl groups, is related to the character theory of the fixed subgroup of the diagram automorphism.

中文翻译：

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对称群与超八面体群的性格关系

我们联系对称群的特征理论 ${\mathbb{小号}}_{2ñ}$ 和 ${\mathbb{小号}}_{2ñ+\mathrm{1个}}$ 与高八面体组的 ${\mathbb{乙}}_{ñ}={（\mathbb{ž}/2）}^{ñ}⋊{\mathbb{小号}}_{ñ}$作为图自同构的还原性基团及其Weyl基的特征理论的一部分，与图自同构的固定子组的特征理论有关。