# On some trivial source Specht modules

## TL;DR

This paper classifies trivial source Specht modules labeled by hook and two-part partitions, providing complete classifications in certain cases and supporting a conjecture in the even characteristic case.

## Contribution

It offers a complete classification of trivial source Specht modules for hook partitions and partial results for two-part partitions, confirming a conjecture in even characteristic.

## Key findings

- Complete classification for hook partitions
- Classification for two-part partitions in odd characteristic
- Partial classification for partitions with 2-weight 2 in even characteristic

## Abstract

The paper presented here focuses on the classification of trivial source Specht modules. We completely classify the trivial source Specht modules labelled by hook partitions. We also classify the trivial source Specht modules labelled by two-part partitions in the odd characteristic case. Moreover, in the even characteristic case, we prove a result for the classification of the trivial source Specht modules labelled by partitions with 2-weight 2, which justifies a conjecture of [16].