On a result of Kiyota, Okuyama and Wada

TL;DR

This paper offers a more conceptual proof of a recent result by Kiyota, Okuyama, and Wada, establishing the uniqueness of a height 0 irreducible Brauer character in each 2-block of a finite symmetric group.

Contribution

It provides a new, more conceptual proof of a known result about the structure of 2-blocks in finite symmetric groups.

Findings

Unique height 0 irreducible Brauer character exists in each 2-block.

The proof is more conceptual and potentially more insightful.

Confirms the structure of 2-blocks in finite symmetric groups.

Abstract

M. Kiyota, T. Okuyama and T. Wada recently proved that each 2-block of a finite symmetric group contains a unique irreducible Brauer character that has height 0. We present a more conceptual proof of this result.