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Counting extensions of Characters of Spin groups, equivariant Jordan decomposition and the McKay Conjecture

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GR2W01 - Counting conjectures and beyond

In the talk I present some new results about the action of automorphisms on characters of Spin groups. For their proofs it is crucial to count and determine characters extending to an overgroup obtained by adding a graph and a field automorphism. A by-product is an equivariant Jordan decomposition for characters of quasi-simple groups. We will also describe the implications for the inductive McKay condition. The whole approach builds on a Malle’s result about the action of automorphisms on cuspidal characters and ensures that a character bijection given by him  can be chosen equivariant in some cases. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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