2011/08/18 by Frieder Ladisch, Ladisch, Frieder
Mathematics · #20C15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C15
paper · pdf · doi:10.48550/arxiv.1108.3777
arxiv created 2011/08/18 · openalex publication_date 2011/08/18 · arxiv updated 2011/08/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 IrrA(N) of irreducible complex characters invariant under the action of A, and the irreducible characters of the centralizer of A in N, Irr(CN(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= NG(A). Let χ∈ IrrA(N) and χ* ∈ Irr(CN(A)) correspond. Then there is a canonical bijection between Irr(G | χ) and Irr(U | χ*) preserving Schur indices. We also give simplified and more conceptual proofs of (known) character correspondences above fully ramified sections.