The ring R(Bn) of virtual C-characters of the hyperoctahedral group Bn
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(Bn) is a homomorphic image. In particular, the concept of Young characters
of Bn arises from a certain set Un of subgroups of Bn, and the Z-basis of R(Bn)
consisting of Young characters, which is presented by L. Geissinger and D.
Kinch [7], forces R(Bn) to be isomorphic to a partial Burnside ring Ω(Bn; Un).
The linear C-characters of Bn are analyzed with reduced Lefschetz invariants
which characterize the unit group of Ω(Bn; Un). The parabolic Burnside ring
PB(Bn) is a subring of Ω(Bn; Un), and the unit group of PB(Bn) is isomorphic
to the four group. The unit group of the parabolic Burnside ring of the even-
signed permutation group Dn is also isomorphic to the four group.
Lefschetz invariants and Young characters for representations of the hyperoctahedral groups
JA_512_1_19
(161.32KB)
