This package, SL2Reps, provides methods for constructing and testing matrix presentations of the representations of SL(2,Z) whose kernels are congruence subgroups of SL(2,Z).

Irreducible representations of prime-power level are constructed individually by using the Weil representations of quadratic modules, and from these a list of all representations of a given degree or level can be produced. The format is designed for the study of modular tensor categories in particular, providing symmetric matrix presentations of each representation.

Installation

To install SL2Reps, first download it from https://snw-0.github.io/sl2-reps/, then place it in the pkg subdirectory of your GAP installation (or in the pkg subdirectory of any other GAP root directory, for example one added with the -l argument).

SL2Reps is then loaded with the GAP command

gap> LoadPackage( "SL2Reps" );

Contact

Siu-Hung Ng, Louisiana State University (rng@math.lsu.edu)
Yilong Wang¹, Louisiana State University (wyl@bimsa.cn)
Samuel Wilson, Louisiana State University (swil311@lsu.edu)

Acknowledgements

This project is partially supported by NSF grant DMS 1664418.

Footnotes

1. Currently at Beijing Institute of Mathematical Science and Applications (BIMSA). ↩