Finding irreducible representation of symmetry operators linearly

TL;DR

This paper introduces a straightforward method to generate matrices of irreducible representations of symmetry operators using only the group multiplication table, aiming to reduce computational effort in eigenvalue problem solutions.

Contribution

It presents a novel, simple approach for deriving irreducible representation matrices solely from the group multiplication table, with a proof of its validity.

Findings

Method effectively generates irreducible representation matrices

Reduces computational time in eigenvalue problem solving

Validated through proof of correctness

Abstract

The main purpose of this paper is providing a simple method to generate the matrices of irreducible representations because it is useful to reduce the computational time of solving the eigenvalue problems. The only information we need to provide for this method is the group-multiplication table, and the proof of validity of this method is also shown in this paper.