Alperin-McKay natural correspondences in solvable and symmetric groups for the prime $p=2$

TL;DR

This paper establishes a canonical correspondence between certain irreducible characters in blocks of solvable and symmetric groups for prime 2, enhancing understanding of character theory in these groups.

Contribution

It constructs a new canonical bijection between height zero characters and their Brauer correspondents, compatible with restriction in symmetric groups.

Findings

Established a canonical correspondence for prime 2

Compatible with restriction in symmetric groups

Advances understanding of character correspondences in group theory

Abstract

Let $G$ be a finite solvable or symmetric group and let $B$ be a $2$-block of $G$. We construct a canonical correspondence between the irreducible characters of height zero in $B$ and those in its Brauer first main correspondent. For symmetric groups our bijection is compatible with restriction of characters.