Character correspondences above fully ramified sections and Schur indices
Abstract
Let N be a finite group of odd order and A a finite group that acts on N such that the orders of N and A are coprime. Isaacs constructed a natural correspondence between the set Irr_A(N) of irreducible complex characters invariant under the action of A, and the irreducible characters of the centralizer of A in N, Irr(C_N(A)). We show that this correspondence preserves Schur indices over the rational numbers. Moreover, suppose that the semidirect product AN is a normal subgroup of the finite group G and set U= N_G(A). Let \chi \in Irr_A(N) and \chi* \in Irr(C_N(A)) correspond. Then there is a canonical bijection between Irr(G | \chi) and Irr(U | \chi*) preserving Schur indices. We also give simplified and more conceptual proofs of (known) character correspondences above fully ramified sections.
Keywords
Cite
@article{arxiv.1108.3777,
title = {Character correspondences above fully ramified sections and Schur indices},
author = {Frieder Ladisch},
journal= {arXiv preprint arXiv:1108.3777},
year = {2011}
}