Quelle _Chapter_Lists.xml Sprache: XML

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


<Chapter Label="Chapter_Lists">
<Heading>Lists of representations</Heading>

<P/>
The <Emph>degree</Emph> of a representation is also known as the <Emph>dimension</Emph>.
The <Emph>level</Emph> of the congruent representation determined by the pair <Math>(S,T)</Math> is equal to the order of <Math>T</Math>.
<P/>
We assign to each representation a <Emph>name</Emph> according to the conventions of <Cite Key="NW76"/>.
<Section Label="Chapter_Lists_Section_Degree">
<Heading>Lists by degree</Heading>

<ManSection>
  <Func Arg="degree" Name="SL2IrrepsOfDegree" />
<Returns>a list of records of the form <Code>rec(S, T, degree, level, name)</Code>.
</Returns>
<Description>
  Constructs a list of all irreps of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>
  that have the given degree.
</Description>
</ManSection>

<ManSection>
  <Func Arg="maximum_degree" Name="SL2IrrepsOfMaxDegree" />
<Returns>a list of records of the form <Code>rec(S, T, degree, level, name)</Code>.
</Returns>
<Description>
  Constructs a list of all irreps of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>
  that have at most the given maximum degree.
</Description>
</ManSection>

</Section>

<Section Label="Chapter_Lists_Section_Level">
<Heading>Lists by level</Heading>

<ManSection>
  <Func Arg="level" Name="SL2IrrepsOfLevel" />
<Returns>a list of records of the form <Code>rec(S, T, degree, level, name)</Code>.
</Returns>
<Description>
  Constructs a list of all irreps of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>
  with the given level.
</Description>
</ManSection>

</Section>

<Section Label="Chapter_Lists_Section_Exceptions">
<Heading>Lists of exceptional representations</Heading>

<ManSection>
  <Func Arg="arg" Name="SL2IrrepsExceptional" />
<Returns>a list of records of the form <Code>rec(S, T, degree, level, name)</Code>.
</Returns>
<Description>
  Constructs a list of the 18 exceptional irreps of <Math>\mathrm{SL}_2(\mathbb{Z})</Math>.
</Description>
</ManSection>

</Section>

</Chapter>

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