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- W4366341373 abstract "We determine the action of the outer automorphism group Out$(G)$ 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 Out$(G)$-equivariant Jordan decomposition of characters (Theorem B). We also prove an extendibility statement, called condition $A(infty)$, see Theorem A. Among the methods used here in the case of groups of type D and $^2$D, we blend the Shintani descent ideas introduced in [CS19, S~3] and an analysis of semisimple classes in the dual group $G^*$ from [CS22]. This enables us to control the action of graph and field automorphisms within Lusztig's rational series of characters and to count extendible characters. Condition $A(infty)$ originates in the program to prove the McKay conjecture using the classification of finite simple groups, see [IMN07]. Using the local results from [MS16], our main theorem implies the McKay conjecture for the prime 3 and all finite groups." @default.
- W4366341373 created "2023-04-20" @default.
- W4366341373 creator A5069367253 @default.
- W4366341373 date "2023-04-14" @default.
- W4366341373 modified "2023-09-30" @default.
- W4366341373 title "Extensions of characters in type D and the inductive McKay condition, II" @default.
- W4366341373 doi "https://doi.org/10.48550/arxiv.2304.07373" @default.
- W4366341373 hasPublicationYear "2023" @default.
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