REPRESENTATIONS OF SYMMETRIC GROUPS

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REPRESENTATIONS OF SYMMETRIC GROUPS

Acknowledgements

Introduction

Representations of the Symmetric Group
Integral Representations
The Seminormal and Orthogonal Representations

Characters of the Symmetric Group
Single Values
Irreducible Characters
Character Table

Representations of the Alternating Group

Characters of the Alternating Group
Single Values
Irreducible Characters
Character Table

Bibliography

DETAILS

Introduction

Representations of the Symmetric Group

Integral Representations
SymmetricRepresentation(pa, pe) : SeqEnum, GrpPermElt -> AlgMatElt
Example RepSym_integral representations (H89E1)

The Seminormal and Orthogonal Representations
SymmetricRepresentationSeminormal(pa, pe) : SeqEnum,GrpPermElt -> AlgMatElt
SymmetricRepresentationOrthogonal(pa, pe) : SeqEnum,GrpPermElt -> AlgMatElt
Example RepSym_semi-orthog (H89E2)

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

Bibliography

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