Abstract
In this paper characters of the normalizer of d-split Levi subgroups in SLn(q) and SUn(q) are parametrized with a particular focus on the Clifford theory between the Levi subgroup and its normalizer. These results are applied to verify the Alperin-McKay conjecture for primes ℓ with ℓ∤6(q2−1) and the Alperin weight conjecture for ℓ-blocks of those quasi-simple groups with abelian defect. The inductive Alperin-McKay condition and inductive Alperin weight condition by the second author are verified for certain blocks of SLn(q) and SUn(q).
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