The units of a partial Burnside ring relative to the Young subgroups of a symmetric group

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• 作者：Fumihito Oda^a ; ^{odaf@math.kindai.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Yugen Takegahara^b ; ^{yugen@mmm.muroran-it.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Tomoyuki Yoshida^c ; ^{ytomoyuki@mub.biglobe.ne.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 19A22 ; secondary ; 20B35 ; 20C15 ; 20C30
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：460
• 期：Complete
• 页码：370-379
• 全文大小：319 K

文摘

The unit group of a partial Burnside ring relative to the Young subgroups of the symmetric group S_n$S_n$ on n   letters is included in the image by the tom Dieck homomorphism. As a consequence of this fact, the alternating character ν_n${\nu }_n$ of S_n$S_n$ is expressed explicitly as a Z$\mathbb{Z}$-linear combinations of permutation characters associated with finite left S_n$S_n$-sets S_n/Y$S_n/Y$ for the Young subgroups Y.