Dade's ordinary conjecture implies the Alperin-McKay conjecture

TL;DR

This paper demonstrates that Dade's ordinary conjecture leads to the proof of the Alperin-McKay conjecture, and discusses methods for identifying canonical height zero characters in nilpotent blocks.

Contribution

It establishes a logical implication from Dade's conjecture to the Alperin-McKay conjecture and introduces techniques for character identification in nilpotent blocks.

Findings

Dade's conjecture implies the Alperin-McKay conjecture.

Methods for identifying height zero characters in nilpotent blocks are proposed.

The paper bridges two important conjectures in representation theory.

Abstract

We show that Dade's ordinary conjecture implies the Alperin-McKay conjecture. We remark that some of the methods can be used to identify a canonical height zero character in a nilpotent block.