On the Inductive Alperin--McKay Conditions in the Maximally Split Case
Résumé
The Alperin-McKay conjecture relates height zero characters of an-block with the ones of its Brauer correspondent. This conjecture has been reduced to the so-called inductive Alperin-McKay conditions about quasi-simple groups by the third author. The validity of those conditions is still open for groups of Lie type. The present paper describes characters of height zero in-blocks of groups of Lie type over a field with q elements when divides q − 1. We also give information about-blocks and Brauer correspondents. As an application we show that quasi-simple groups of type C over F q satisfy the inductive Alperin-McKay conditions for primes ≥ 5 and dividing q − 1. Some methods to that end are adapted from [MS16].
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