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Magma
Computer • algebra
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Introduction
Representations of the Symmetric Group
Integral Representations
SymmetricRepresentation(pa, pe) : SeqEnum, GrpPermElt -> AlgMatElt
Example
RepSym_integral representations (H99E1)
The Seminormal and Orthogonal Representations
SymmetricRepresentationSeminormal(pa, pe) : SeqEnum,GrpPermElt -> AlgMatElt
SymmetricRepresentationOrthogonal(pa, pe) : SeqEnum,GrpPermElt -> AlgMatElt
Example
RepSym_semi-orthog (H99E2)
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
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V2.28, 13 July 2023