Using Hook Schur Functions to Compute Matrix Cocharacters

TL;DR

This paper introduces a method using hook Schur functions to compute matrix cocharacters in specific hook shapes, demonstrated through the example of 3x3 matrices in a 1x2 hook.

Contribution

It presents a novel application of hook Schur functions for calculating matrix cocharacters in hook shapes, expanding computational techniques in invariant theory.

Findings

Successfully computed cocharacters for 3x3 matrices in the 1x2 hook

Demonstrated the effectiveness of hook Schur functions in this context

Provided explicit examples and calculations

Abstract

We use hook Schur functions to compute trace cocharacters of matrices in hooks. As an example we compute the cocharacters of 3 x 3 matrices in the one by two hook.