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 );
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