The paper Affine characters at negative level and elliptic genera of non-critical strings, written in collaboration with David Jaramillo Duque, requires, as the title indicates, computing affine characters at negative level. The algorithm we use is explained in Appendix B of the paper.

It is implemented in this SageMath class.

A short Jupyter notebook to explain some of the workings of this class can be found here.

The characters which occur in the elliptic genera we compute can be downloaded by clicking on this link.

The characters are given in the form \(\text{ch}\, R\), in the notation of Appendix B. We have organized the characters in directories with names G_n_characters indicating charactes of the affine Lie algebra G at level \(-n\). Each directory contains text files with names affine_char_G_{a1, ..., an}.txt, with the highest weight of the representation indicated in curly brackets. The order of the entries follows the conventions of SageMath for numbering the nodes of Dynkin diagrams. The text files are readable by Mathematica. They contain a list of lists. A list entry {0,2,0,0,0,1} in the file affine_char_F4_{-9,2,0,0,0}.txt e.g. indicates that the affine character to F4 with highest weight \(-9 \lambda_0 + 2 \lambda_1\) has a contribution \[ \{0,2,0,0,0,1\}\quad \rightarrow \quad 1*q^0 \chi_{2,0,0,0}\,,\] where \(\chi_{2,0,0,0}\) is the finite character for the representation with highest weight \(2\lambda_1\).