GAP (SL2Reps) - Chapter 4: Lists of representations

Goto Chapter: Top 1 2 3 4 5 Bib Ind
[Top of Book] [Contents] [Previous Chapter] [Next Chapter]

[MathJax off]

4 Lists of representations
4.1 Lists by degree
4.1-1 SL2IrrepsOfDegree
4.1-2 SL2IrrepsOfMaxDegree
4.2 Lists by level
4.2-1 SL2IrrepsOfLevel
4.3 Lists of exceptional representations
4.3-1 SL2IrrepsExceptional

### 4 Lists of representations

The degree of a representation is also known as the dimension. The level of the congruent representation determined by the pair \((S,T)\) is equal to the order of \(T\).

We assign to each representation a name according to the conventions of [NW76].

#### 4.1 Lists by degree

##### 4.1-1 SL2IrrepsOfDegree

`‣ SL2IrrepsOfDegree`( degree ) | ( function )

Returns: a list of records of the form `rec(S, T, degree, level, name)`.

Constructs a list of all irreps of \(\mathrm{SL}_2(\mathbb{Z})\) that have the given degree.

##### 4.1-2 SL2IrrepsOfMaxDegree

`‣ SL2IrrepsOfMaxDegree`( maximum_degree ) | ( function )

Returns: a list of records of the form `rec(S, T, degree, level, name)`.

Constructs a list of all irreps of \(\mathrm{SL}_2(\mathbb{Z})\) that have at most the given maximum degree.

#### 4.2 Lists by level

##### 4.2-1 SL2IrrepsOfLevel

`‣ SL2IrrepsOfLevel`( level ) | ( function )

Returns: a list of records of the form `rec(S, T, degree, level, name)`.

Constructs a list of all irreps of \(\mathrm{SL}_2(\mathbb{Z})\) with the given level.

#### 4.3 Lists of exceptional representations

##### 4.3-1 SL2IrrepsExceptional

`‣ SL2IrrepsExceptional`( arg ) | ( function )

Returns: a list of records of the form `rec(S, T, degree, level, name)`.

Constructs a list of the 18 exceptional irreps of \(\mathrm{SL}_2(\mathbb{Z})\).

[Top of Book] [Contents] [Previous Chapter] [Next Chapter]
Goto Chapter: Top 1 2 3 4 5 Bib Ind

generated by GAPDoc2HTML