Brauer特征标的诱导与限制

Induction and Restriction of Brauer Characters

设HG且χ∈Irr(G),φ∈IBr(G),Cossey等给出了χ=βG对χH的每个不可约成分β都成立的一个充分条件;同时,给定β∈Irr(H),也得到了一个使β=χH对βG的每个不可约成分χ都成立的条件.我们通过讨论φ的零化元,给出了(φH)G是φ的倍数的一个刻画.对偶地,对于α∈IBr(H),也给出了(αG)H是α的倍数的一个刻画.

Let HC_G,ZE Irr（G） and φ∈E IBr（G）. Cossey obtain a sufficient condition for X=β G, where β∈ Irr（ZH ）. Simultaneously, given a character β∈ Irr（H）,they get a condition satisfy β=XH for every irreducible constituent X of βG. In this paper we determine when it happens that （φH）G; is a multiple of φ by investigating the vanishing elements of φ. Dually,we give a description to determine that （αG）H is a multiple of a for α∈ IBr（H）.