Quelle _Chapter_Introduction.xml Sprache: XML

<?xml version="1.0" encoding="UTF-8"?>


<Chapter Label="Chapter_Introduction">
<Heading>Introduction</Heading>

<P/>
This package, <Code>SL2Reps</Code>, provides methods for constructing and testing matrix
presentations of the representations of <Math>\mathrm{SL}_2(\mathbb{Z})</Math> whose kernels are congruence subgroups of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>.
<P/>
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 <Math>(S,T)</Math>, where <Math>S</Math> is a symmetric,
unitary matrix and <Math>T</Math> is a diagonal matrix of finite order; this format is designed for the study of modular tensor categories in particular.
<P/>
<Section Label="Chapter_Introduction_Section_Installation">
<Heading>Installation</Heading>

<P/>
To install <Code>SL2Reps</Code>, first download it from <URL>https://snw-0.github.io/sl2-reps/</URL>, then place it in the <Code>pkg</Code>
subdirectory of your GAP installation (or in the <Code>pkg</Code> subdirectory of any other GAP
root directory, for example one added with the <Code>-l</Code> argument).
<P/>
<Code>SL2Reps</Code> is then loaded with the GAP command
<P/>
<Code>gap> LoadPackage( "SL2Reps" );</Code>
<P/>
</Section>

<Section Label="Chapter_Introduction_Section_Usage">
<Heading>Usage</Heading>

<P/>
Specific irreducible representations may be constructed via the methods in Chapter <Ref Chap="Chapter_Irreps"/>, while lists of irreducible representations with a given degree or level may be constructed with those in Chapter <Ref Chap="Chapter_Lists"/>.
<P/>
This package uses an <Code>InfoClass</Code>, <Code>InfoSL2Reps</Code>. It may be set to <Code>0</Code> (silent),
<Code>1</Code> (info), or <Code>2</Code> (verbose). To change it, use
<P/>
<Code>gap> SetInfoLevel( InfoSL2Reps, k );</Code>
<P/>
</Section>

</Chapter>

quality100%

¤ Dauer der Verarbeitung: 0.18 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.