On the Alperin-McKay conjecture for 2-blocks of maximal defect

TL;DR

This paper proves the Alperin-McKay conjecture for 2-blocks of maximal defect, focusing on the inductive condition for groups of Lie type in odd characteristic, advancing understanding in modular representation theory.

Contribution

It verifies the conjecture for a broad class of blocks by establishing the inductive condition for principal 2-blocks of Lie type groups in odd characteristic.

Findings

Alperin-McKay conjecture holds for 2-blocks of maximal defect

Inductive condition verified for principal 2-blocks of Lie type groups in odd characteristic

Progress towards the conjecture's general proof

Abstract

In this paper, we show that the Alperin-McKay conjecture holds for 2-blocks of maximal defect. A major step in the proof is the verification of the inductive Alperin-McKay condition for the principal 2-block of groups of Lie type in odd characteristic.