# Representations of Symmetric Groups

- [Introduction](introduction.md)

- [Representations of the Symmetric Group](repsym.md)

  - [Integral Representations](repsym.md#integral-representations)

    - [`SymmetricRepresentation(pa, pe): SeqEnum, GrpPermElt → AlgMatElt`](repsym.md#function-symmetricrepresentation-seqenum-grppermelt)

    - [`Example: integral representations`](repsym.md#example-ex-be2f6e)

  - [The Seminormal and Orthogonal Representations](repsym.md#the-seminormal-and-orthogonal-representations)

    - [`SymmetricRepresentationSeminormal(pa, pe): SeqEnum, GrpPermElt → AlgMatElt`](repsym.md#function-symmetricrepresentationseminormal-seqenum-grppermelt)

    - [`SymmetricRepresentationOrthogonal(pa, pe): SeqEnum, GrpPermElt → AlgMatElt`](repsym.md#function-symmetricrepresentationorthogonal-seqenum-grppermelt)

    - [`Example: Semi Orthog`](repsym.md#example-ex-5248de)

- [Characters of the Symmetric Group](charsym.md)

  - [Single Values](charsym.md#single-values)

    - [`SymmetricCharacterValue(pa, pe): SeqEnum, GrpPermElt → RngElt`](charsym.md#function-symmetriccharactervalue-seqenum-grppermelt)

  - [Irreducible Characters](charsym.md#irreducible-characters)

    - [`SymmetricCharacter(pa): SeqEnum → AlgChtrElt`](charsym.md#function-symmetriccharacter-seqenum)

  - [Character Table](charsym.md#character-table)

    - [`SymmetricCharacterTable(d): RngIntElt → SeqEnum`](charsym.md#function-symmetriccharactertable-rngintelt)

- [Representations of the Alternating Group](repalt.md)

- [Characters of the Alternating Group](charalt.md)

  - [Single Values](charalt.md#single-values)

    - [`AlternatingCharacterValue(pa, pe): SeqEnum, GrpPermElt → RngElt`](charalt.md#function-alternatingcharactervalue-seqenum-grppermelt)

    - [`AlternatingCharacterValue(pa, i, pe): SeqEnum, RngIntElt, GrpPermElt → RngElt`](charalt.md#function-alternatingcharactervalue-seqenum-rngintelt-grppermelt)

  - [Irreducible Characters](charalt.md#irreducible-characters)

    - [`AlternatingCharacter(pa): SeqEnum → AlgChtrElt`](charalt.md#function-alternatingcharacter-seqenum)

    - [`AlternatingCharacter(pa, i): SeqEnum, RngIntElt → AlgChtrElt`](charalt.md#function-alternatingcharacter-seqenum-rngintelt)

  - [Character Table](charalt.md#character-table)

    - [`AlternatingCharacterTable(d): RngIntElt → SeqEnum`](charalt.md#function-alternatingcharactertable-rngintelt)