Descent equalities and the inductive McKay condition for types B and E

2019/03/27 by Cabanes, Marc, Späth, Britta · 3 citations
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1903.11667

Abstract

We establish the inductive McKay condition introduced by Isaacs-Malle-Navarro \citeIMN for finite simple groups of Lie types \tB_l (l≥ 2), \tE₆, ²\tE₆ and \tE₇, thus leaving open only the types \tD and ²\tD. We bring to the methods previously used by the authors for type \tC \citeCS17C some descent arguments using Shintani's norm map. This provides for types different from \tA, \tD, ²\tD a uniform proof of the so-called global requirement of the criterion given by the second author in \cite[2.12]S12. The local requirements from that criterion are verified through a detailed study of the normalizers of relevant Levi subgroups and their characters.

Cited by

• The Picky Conjecture for groups of Lie type
• The Isaacs--Navarro Galois conjecture
• Generic weights for finite reductive groups

Related

• Towards the inductive McKay--Navarro Condition for groups of Lie type
• Inductive Feit and Galois-McKay conditions for some small-rank simple groups of Lie Type
• Inductive McKay condition for finite simple groups of type C
• On equivariant bijections relative to the defining characteristic
• Equivariant character correspondences and inductive McKay condition for\n type A