Character -- the class of all characters of finite group representations

Functions and methods returning an object of class Character:

• character -- compute characters of finite group action
• Character Array -- homological shift
• character(ActionOnComplex) -- compute all Betti characters of minimal free resolution
• character(ActionOnComplex,ZZ) -- compute Betti characters of minimal free resolution
• character(ActionOnGradedModule,List) -- compute characters of graded components of a module
• character(ActionOnGradedModule,ZZ) -- see character(ActionOnGradedModule,List) -- compute characters of graded components of a module
• character(ActionOnGradedModule,ZZ,ZZ) -- see character(ActionOnGradedModule,List) -- compute characters of graded components of a module
• character(CharacterDecomposition,CharacterTable) -- recover character from decomposition
• CharacterDecomposition * CharacterTable -- see character(CharacterDecomposition,CharacterTable) -- recover character from decomposition
• character(PolynomialRing,ZZ,HashTable) -- construct a character
• Character ++ Character -- see directSum(Character) -- direct sum of characters
• dual(Character,List) -- see dual -- dual character
• dual(Character,RingMap) -- see dual -- dual character
• Character ** Character -- see tensor(Character,Character) -- tensor product of characters
• tensor(Character,Character) -- tensor product of characters

Methods that use an object of class Character:

• Character / CharacterTable -- see decomposeCharacter -- decompose a character into irreducible characters
• decomposeCharacter(Character,CharacterTable) -- see decomposeCharacter -- decompose a character into irreducible characters
• directSum(Character) -- direct sum of characters
• Character == Character -- see Equality checks -- compare actions and characters
• net(Character) -- format for printing, as a net

For the programmer

The object Character is a type, with ancestor classes HashTable < Thing.

The source of this document is in BettiCharacters.m2:2846:0.