RepLAB: a computational/numerical approach to representation theory

TL;DR

This paper introduces RepLAB, a MATLAB/Octave toolbox that efficiently decomposes finite-dimensional representations of compact groups with minimal group information, facilitating applications like semidefinite programming.

Contribution

The paper presents a novel computational toolbox that simplifies the decomposition of group representations, requiring little prior information about the groups or representations.

Findings

Effective decomposition of representations with minimal group info

Applications demonstrated in semidefinite programming

Toolbox available for practical use

Abstract

We present a MATLAB/Octave toolbox to decompose finite dimensionial representations of compact groups. Surprisingly, little information about the group and the representation is needed to perform that task. We discuss applications to semidefinite programming.