A constructive method for decomposing real representations

TL;DR

This paper introduces a constructive algorithm for decomposing finite-dimensional representations of semisimple real Lie algebras, demonstrating its application with an example and discussing its implementation in GAP4.

Contribution

It presents a novel constructive method for decomposing real Lie algebra representations and details its implementation in a computer algebra system.

Findings

Successful decomposition of representations demonstrated with an example

Implementation of the algorithm in GAP4 shown to be feasible

Provides a new computational tool for Lie algebra representation analysis

Abstract

A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the computer algebra system {\sf GAP}4.