Extensions of characters in type D and the inductive McKay condition, II

2023/04/14 by Britta Späth, Späth, Britta · 3 citations
Mathematics · #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2304.07373

Abstract

We determine the action of the automorphism group Aut(G) on the set of irreducible characters Irr(G) for all finite quasi-simple groups G. For groups of Lie type, this includes the construction of an Aut(G)-equivariant Jordan decomposition of characters (Theorem B). We prove a property called A(∞) which includes an extendibility statement, known previously in types not D (Theorem A). Our methods blend here Shintani descent ideas introduced for type B along with an analysis of semisimple classes in the dual group G^*. The condition A(∞) originates in the program to prove the McKay conjecture using the classification of finite simple groups. Theorem C establishes the McKay conjecture for the prime 3.

Cited by

• The McKay conjecture with coprime group automorphisms and the Okuyama-Wajima argument
• McKay bijections and character degrees
• Generic weights for finite reductive groups

Related

• Extensions of characters in type D and the inductive McKay condition, I
• Equivariant character correspondences and inductive McKay condition for type A
• The Navarro refinement of the McKay conjecture for finite groups of Lie type in defining characteristic
• Action of automorphisms on irreducible characters of groups of type \textsfA
• Cuspidal characters and automorphisms