arXiv: Representation Theory | 2019
Descent equalities and the inductive McKay condition for types B and E
Abstract
We establish the inductive McKay condition introduced by Isaacs-Malle-Navarro \\cite{IMN} for finite simple groups of Lie types $\\tB_l$ ($l\\geq 2$), $\\tE_6$, $^2\\tE_6$ and $\\tE_7$, thus leaving open only the types $\\tD$ and $^2\\tD$. We bring to the methods previously used by the authors for type $\\tC$ \\cite{CS17C} 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.