More counting for the counting conjectures

The action of automorphisms on the irreducible characters of finite quasi-simple groups of Lie type is a well-known open problem. For symplectic groups this problem could be solved via a technical counting argument. We give a more structural explanation of this counting that applies to other types. Using this the inductive McKay condition can be verified for certain simple groups of Lie type. This is joint work with M. Cabanes.

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