(Ir-)reducibility of some tensor products of k(e10)-representations

Abstract

This is a collection of codes written in Sagemath 9.0 that provide an implementation of certain so-called "higher spin representations" of the maximal compact subalgebra k(e10) of the Kac-Moody-algebra e10. Furthermore, the code analyzes (ir-)reducibility of these representations by exploiting their decomposition w.r.t. the subalgebra so(10) of k(e10). The collection includes several codes, folders with the representation matrices as well as the so(10)-modules into which the respective k(e10)-modules split. These codes were used to obtain the results of section 6.1 of the author's PhD-thesis "Higher Spin representations in Kac-Moody-Theory". The notebooks (IPYNB-files) are intended to be used with SageMath 9.0 Notebook. The other SAGE-files are scripts, some of them are loaded within the notebooks. The script "serial_run" is intended for use on a computer cluster. As the computation is set up in a serial manner and does not benefit from parallelization, a serial queue is recommended.