This package, SL2Reps, provides methods for constructing and testing matrix presentations of the representations of \(\mathrm{SL}_2(\mathbb{Z})\) whose kernels are congruence subgroups of \(\mathrm{SL}_2(\mathbb{Z})\).
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. Each representation is represented by a pair \((S,T)\), where \(S\) is a symmetric, unitary matrix and \(T\) is a diagonal matrix of finite order; this format is designed for the study of modular tensor categories in particular.
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" );
Specific irreducible representations may be constructed via the methods in Chapter 3, while lists of irreducible representations with a given degree or level may be constructed with those in Chapter 4.
This package uses an InfoClass, InfoSL2Reps. It may be set to 0 (silent), 1 (info), or 2 (verbose). To change it, use
gap> SetInfoLevel( InfoSL2Reps, k );
generated by GAPDoc2HTML