On the Alperin-McKay conjecture for simple groups of type A

摘要

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 inverted iota 6(q(2) - 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). (C) 2020 Published by Elsevier Inc.