McKay bijections and decomposition numbers

TL;DR

This paper proves that for p-solvable groups, there exists a McKay bijection that preserves the decomposition numbers for linear characters, linking character theory and modular representation theory.

Contribution

It establishes the existence of a McKay bijection respecting decomposition numbers in p-solvable groups, a new connection in modular representation theory.

Findings

Existence of McKay bijection for p-solvable groups

Bijection respects decomposition numbers for linear characters

Bridges character theory with modular representation theory

Abstract

If $G$ is $p$-solvable, we prove that there exists a McKay bijection that respects the decomposition numbers $d_{\chi\varphi}$, whenever $\varphi$ is linear.