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

JOURNAL OF ALGEBRA

卷:460

Article

Oda, Fumihito¹  Takegahara, Yugen²  Yoshida, Tomoyuki³ 

[1] Kindai Univ, Dept Math, Higashiosaka, Osaka 5778502, Japan

[2] Muroran Inst Technol, 27-1 Mizumoto, Muroran, Hokkaido 0508585, Japan

[3] Hokusei Gakuen Univ, Grad Sch Econ, Atsubetsu Ku, 2-3-1 Ohyachi Nishi, Sapporo, Hokkaido 0048631, Japan

关键词: Burnside ring;    Character ring;    Lefschetz invariant;    Symmetric group;    Young subgroup;    tom Dieck homomorphism;   

DOI  :  10.1016/j.jalgebra.2016.05.002

来源: Elsevier

【 摘 要 】

The unit group of a partial Burnside ring relative to the Young subgroups of the symmetric group S-n on n letters is included in the image by the tom Dieck homomorphism. As a consequence of this fact, the alternating character nu(n) of S-n is expressed explicitly as a Z-linear combinations of permutation characters associated with finite left S-n-sets S-n/Y for the Young subgroups Y. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free