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

2019/01/14 by Julian Brough, Brough, Julian, Britta Späth +1
Computer Science · Mathematics · #20C20 (20C33 20C34) #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1901.04591

openalex publication_date 2019/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper characters of the normaliser of d-split Levi subgroups in \mathrm SL_n(q) and \mathrm SU_n(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\nmid 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 \mathrm SL_n(q) and \mathrm SU_n(q).

Related

• Characters of normalisers of d-split Levi subgroups in Sp2n(q)
• On the Inductive Alperin-McKay Conditions in the Maximally Split Case
• The inductive blockwise Alperin weight condition for G₂(q) and ³D₄(q)
• A criterion for the inductive Alperin weight condition
• Quasi-isolated blocks and the Alperin-McKay conjecture