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1 Introduction
 1.1 Installation
 1.2 Usage

1 Introduction

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.

1.1 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" );

1.2 Usage

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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