Representations of Symmetric Groups

• Introduction
• Representations of the Symmetric Group
  • Integral Representations
    • SymmetricRepresentation(pa, pe): SeqEnum, GrpPermElt → AlgMatElt
    • Example: integral representations
  • The Seminormal and Orthogonal Representations
    • SymmetricRepresentationSeminormal(pa, pe): SeqEnum, GrpPermElt → AlgMatElt
    • SymmetricRepresentationOrthogonal(pa, pe): SeqEnum, GrpPermElt → AlgMatElt
    • Example: Semi Orthog
• Characters of the Symmetric Group
  • Single Values
    • SymmetricCharacterValue(pa, pe): SeqEnum, GrpPermElt → RngElt
  • Irreducible Characters
    • SymmetricCharacter(pa): SeqEnum → AlgChtrElt
  • Character Table
    • SymmetricCharacterTable(d): RngIntElt → SeqEnum
• Representations of the Alternating Group
• Characters of the Alternating Group
  • Single Values
    • AlternatingCharacterValue(pa, pe): SeqEnum, GrpPermElt → RngElt
    • AlternatingCharacterValue(pa, i, pe): SeqEnum, RngIntElt, GrpPermElt → RngElt
  • Irreducible Characters
    • AlternatingCharacter(pa): SeqEnum → AlgChtrElt
    • AlternatingCharacter(pa, i): SeqEnum, RngIntElt → AlgChtrElt
  • Character Table
    • AlternatingCharacterTable(d): RngIntElt → SeqEnum