Lefschetz invariants and Young characters for representations of the hyperoctahedral groups

JOURNAL OF ALGEBRA

卷:512

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;    Hyper octahedral group;    Lefschetz invariant;    Parabolic subgroup;    Sign character;    Symmetric group;    Young subgroup;   

DOI  :  10.1016/j.jalgebra.2018.07.001

来源: Elsevier

【 摘 要 】

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 Omega(B-n, U-n). The linear C-characters of B-n are analyzed with reduced Lefschetz invariants which characterize the unit group of Omega(B-n, U-n). The parabolic Burnside ring PB(B-n) is a subring of Omega(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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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