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SchurRings : Index
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centralizerSize
-- Size of the centralizer of a permutation
centralizerSize(List)
-- Size of the centralizer of a permutation
ClassFunction
-- The class of all Class functions
classFunction
-- Converts symmetric function to class function
ClassFunction * ClassFunction
-- The class of all Class functions
ClassFunction * Number
-- The class of all Class functions
ClassFunction * RingElement
-- The class of all Class functions
ClassFunction + ClassFunction
-- The class of all Class functions
ClassFunction - ClassFunction
-- The class of all Class functions
ClassFunction == ClassFunction
-- The class of all Class functions
classFunction(BasicList)
-- Character of irreducible representation of symmetric group
classFunction(RingElement)
-- Converts symmetric function to class function
coefficientRing(SchurRing)
-- Coefficient ring of a Schur ring
degree(ClassFunction)
-- Degree of virtual character
dim(List,SchurRingElement)
-- dimension of representation
dim(SchurRingElement)
-- dimension of representation
dim(Thing,SchurRingElement)
-- dimension of representation
EHPVariables
-- Specifies sequence of symbols representing e-, h-, and p-functions
EorH
-- e- or h- representation of Jacobi-Trudi determinant
eVariable
-- Elementary symmetric functions in a Symmetric ring
GroupActing
-- Specifies the group that is acting
hVariable
-- Complete symmetric functions in a Symmetric ring
internalProduct
-- Internal product of symmetric functions/class functions
internalProduct(ClassFunction,ClassFunction)
-- Tensor product of virtual representations
internalProduct(RingElement,RingElement)
-- Kronecker product of symmetric functions
jacobiTrudi
-- Jacobi-Trudi determinant
jacobiTrudi(...,EorH=>...)
-- e- or h- representation of Jacobi-Trudi determinant
jacobiTrudi(...,Memoize=>...)
-- Store values of the jacobiTrudi function.
jacobiTrudi(BasicList,Ring)
-- Jacobi-Trudi determinant
Memoize
-- Option to record values of the jacobiTrudi function
Number * ClassFunction
-- The class of all Class functions
numgens(SchurRing)
-- Number of generators of Schur ring.
partitions(Set,BasicList)
-- Partitions of a set
plethysm
-- Plethystic operations on representations
plethysm(BasicList,ClassFunction)
-- Plethystic operations on class functions
plethysm(BasicList,RingElement)
-- Plethystic operations on representations
plethysm(RingElement,ClassFunction)
-- Plethystic operations on class functions
plethysm(RingElement,RingElement)
-- Plethystic operations on representations
pVariable
-- Power-sum symmetric functions in a Symmetric ring
RingElement * ClassFunction
-- The class of all Class functions
scalarProduct
-- Standard pairing on symmetric functions/class functions
scalarProduct(ClassFunction,ClassFunction)
-- Standard scalar product of class functions
scalarProduct(RingElement,RingElement)
-- Standard scalar product of symmetric functions
schurLevel
-- Number of SchurRings the ring is a tensor product of.
schurLevel(Ring)
-- Number of SchurRings the ring is a tensor product of.
schurResolution
-- Compute an ``approximate'' equivariant resolution of a module.
schurResolution(...,DegreeLimit=>...)
-- Specifies the maximal degree of syzygies to be computed
schurResolution(...,SyzygyLimit=>...)
-- Specifies the number of syzygy modules to be computed
schurResolution(RingElement,List)
-- Compute an ``approximate'' equivariant resolution of a module.
schurResolution(RingElement,List,List)
-- Compute an ``approximate'' equivariant resolution of a module.
SchurRing
-- The class of all Schur rings
schurRing
-- Make a SchurRing
SchurRing _ List
-- The class of all Schur rings
SchurRing _ Sequence
-- The class of all Schur rings
SchurRing _ ZZ
-- The class of all Schur rings
schurRing(...,EHPVariables=>...)
-- Specifies sequence of symbols representing e-, h-, and p-functions
schurRing(...,GroupActing=>...)
-- Specifies the group that is acting
schurRing(...,SVariable=>...)
-- Specifies symbol representing s-functions
schurRing(Ring)
-- The Schur ring corresponding to a given Symmetric ring.
schurRing(Ring,Symbol)
-- Make a SchurRing
schurRing(Ring,Symbol,ZZ)
-- Make a SchurRing
schurRing(Ring,Thing)
-- Make a SchurRing
schurRing(Ring,Thing,ZZ)
-- Make a SchurRing
schurRing(Thing)
-- Make a SchurRing
schurRing(Thing,ZZ)
-- Make a SchurRing
SchurRingElement
-- A type describing elements of a SchurRing
SchurRingIndexedVariableTable
SchurRingIndexedVariableTable _ Thing
SchurRings
-- Rings representing irreducible representations of general linear or symmetric groups
SVariable
-- Specifies symbol representing s-functions
symmetricFunction
-- Converts class function to symmetric function
symmetricFunction(ClassFunction,Ring)
-- Converts class function to symmetric function
symmetricRing
-- Make a Symmetric ring
symmetricRing(...,EHPVariables=>...)
-- Specifies sequence of symbols representing e-, h-, and p-functions
symmetricRing(...,GroupActing=>...)
-- Specifies the group that is acting
symmetricRing(...,SVariable=>...)
-- Specifies symbol representing s-functions
symmetricRing(Ring)
-- The Symmetric ring corresponding to a given (Schur) ring.
symmetricRing(Ring,ZZ)
-- Make a Symmetric ring
symmetricRing(ZZ)
-- Make a Symmetric ring
toE
-- Elementary symmetric (e-) basis representation
toE(RingElement)
-- Elementary symmetric (e-) basis representation
toH
-- Complete symmetric (h-) basis representation
toH(RingElement)
-- Complete symmetric (h-) basis representation
toP
-- Power-sum (p-) basis representation
toP(RingElement)
-- Power-sum (p-) basis representation
toS
-- Schur (s-) basis representation
toS(RingElement)
-- Schur (s-) basis representation
toS(RingElement,SchurRing)
-- Schur (s-) basis representation