Alperin–McKay–Navarro conjecture

Establish the Alperin–McKay–Navarro conjecture, a refinement of the Alperin–McKay framework relating characters in principal p-blocks and the corresponding normalizer blocks with compatible Galois action, whose validity would imply broader consequences including those discussed in the paper.

Background

The authors state that their main equivalence for almost simple groups (linking 2-generation of Sylow 3-subgroups to σ-fixed height-zero characters in the principal block) would be a consequence of the Alperin–McKay–Navarro conjecture.

This conjecture is a well-known open problem in block theory and character theory, and its resolution would have far-reaching implications for local/global correspondences.