Equivariant chararacter bijections and the Alperin-McKay conjecture

TL;DR

This paper verifies the inductive Alperin-McKay condition for isolated blocks of groups of Lie type B and C, completing the proof for these groups and advancing the understanding of the conjecture.

Contribution

It completes the verification of the inductive Alperin-McKay condition for groups of Lie type B and C, a key step in the broader conjecture.

Findings

Verification of the inductive Alperin-McKay condition for these groups

Advancement in understanding the Alperin-McKay conjecture

Completion of the proof for groups of Lie type B and C

Abstract

In this paper we consider the inductive Alperin--McKay condition for isolated blocks of groups of Lie type $B$ and $C$. This finishes the verification of the inductive condition for groups of this type.