幻表示诱导的Character对应
Character correspondences induced by magic representations
摘要：
设G是有限群，K是G的正规子群，H是G = HK的子群，L = H \cap K.设θ \in Irr K和θ \in Irr L，且θ_L中有重数n > 0的重数n.在这种情况下，定义了H/L上的一个n次射影表示;如果这个表示是普通的，则它产生Irr（G）之间的一个双射|θ）和Irr（H|）。在此双射下的值和舒尔指数的字段的行为进行了描述。一个模块化的版本的主要结果证明。证明了当n与H/L的阶数互质时，该理论成立.最后，假设P <= G是一个p-群，P \cap K = 1，PK在G中正规，H = N_G（P），且θ和θ_p属于p-亏零块，它们是关于群P的Brauer对应.则F_p[G]或Q_p[G]中位于θ上的每个块都与它关于P的Brauer对应是Morita-等价的.这加强了Turull [在Glauberman信件上方，数学进展。217（2008），2170--2205]。
英文摘要：
Let G be a finite group, K a normal subgroup of G and H a subgroup such that G = HK, and set L = H \cap K. Suppose θ\in Irr K and ϕ\in Irr L, and ϕ occurs in θ_L with multiplicity n > 0. A projective representation of degree n on H/L is defined in this situation; if this representation is ordinary, it yields a bijection between Irr(G | θ) and Irr(H | ϕ). The behavior of fields of values and Schur indices under this bijection is described. A modular version of the main result is proved. We show that the theory applies if n and the order of H/L are coprime. Finally, assume that P <= G is a p-group with P \cap K = 1 and PK normal in G, that H = N_G(P), and that θ and ϕ belong to blocks of p-defect zero which are Brauer correspondents with respect to the group P. Then every block of F_p[G] or Q_p[G] lying over θ is Morita-equivalent to its Brauer correspondent with respect to P. This strengthens a result of Turull [Above the Glauberman correspondence, Advances in Math. 217 (2008), 2170--2205].
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