Alperin-McKay conjecture for the Chevalley groups \(G_ 2(q)\) (Q1327027)

The Alperin-McKay conjecture states that if \(B\) is an \(r\)-block of a finite group \(G\) with defect group \(D\) and \(b\) is its Brauer correspondent in the normalizer of \(D\), then \(B\) and \(b\) have the same number of ordinary irreducible characters of height 0. This conjecture is verified for the groups mentioned in the title. In addition it is shown that if \(D\) is non-abelian, then the number of characters of height 0 equals \(| D : D'|\), where \(D'\) is the commutator subgroup of \(D\). This gives further evidence for a conjecture by the reviewer.