Composition factors of 2-parts spin representations of symmetric groups

TL;DR

This paper investigates the composition factors of the modulo p reduction of spin irreducible representations of symmetric group coverings, focusing on partitions with two parts, and determines some related decomposition numbers.

Contribution

It provides a detailed analysis of the composition factors for these specific spin representations and computes certain decomposition numbers, advancing understanding of modular representation theory.

Findings

Identified composition factors for the modulo p reduction of spin representations.

Computed specific decomposition numbers for these representations.

Enhanced understanding of modular properties of symmetric group coverings.

Abstract

Given an odd prime $p$, we identify composition factors of the reduction modulo $p$ of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers.