SchurRings : Index

• Basis -- Specifies the basis to use for a Schur ring
• branch -- Restrict a Schur, Sp, or O character along a two-factor subgroup
• branch(RingElement,SchurRing,SchurRing) -- Restrict a Schur, Sp, or O character along a two-factor subgroup
• branch(RingElement,ZZ,ZZ) -- Restrict a Schur, Sp, or O character along a two-factor subgroup
• 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
• convert -- Universal dispatcher for converting between Schur ring flavors
• convert(RingElement,Ring) -- Universal dispatcher for converting between Schur ring flavors
• 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
• kostkaNumber -- Compute a Kostka number
• kostkaNumber(BasicList,BasicList) -- Compute a Kostka number
• Memoize -- Option to record values of the jacobiTrudi function
• modificationRule -- Apply the Sam-Snowden-Weyman modification rule
• Number * ClassFunction -- The class of all Class functions
• numgens(SchurRing) -- Number of generators of Schur ring.
• OddOrEven -- Select type $B_n$ or type $D_n$ for an orthogonal 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(...,Basis=>...) -- Specifies the basis to use for a Schur ring
• schurRing(...,EHPVariables=>...) -- Specifies sequence of symbols representing e-, h-, and p-functions
• schurRing(...,GroupActing=>...) -- Specifies the group that is acting
• schurRing(...,OddOrEven=>...) -- Select type $B_n$ or type $D_n$ for an orthogonal Schur ring
• 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
• specialize -- Specialize a stable character to a finite rank
• specialize(...,OddOrEven=>...) -- Select type $B_n$ or type $D_n$ for an orthogonal Schur ring
• specialize(RingElement,List) -- Specialize a stable character to a finite rank
• specialize(RingElement,ZZ) -- Specialize a stable character to a finite rank
• 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(...,Basis=>...) -- Specifies the basis to use for a Schur ring
• symmetricRing(...,EHPVariables=>...) -- Specifies sequence of symbols representing e-, h-, and p-functions
• symmetricRing(...,GroupActing=>...) -- Specifies the group that is acting
• symmetricRing(...,OddOrEven=>...) -- Select type $B_n$ or type $D_n$ for an orthogonal Schur ring
• 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
• toGL -- Express an element in the plain GL Schur basis
• toGL(RingElement) -- Express an element in the plain GL Schur basis
• toGL(RingElement,SchurRing) -- Express an element in the plain GL Schur basis
• toH -- Complete symmetric (h-) basis representation
• toH(RingElement) -- Complete symmetric (h-) basis representation
• toM -- Monomial (m-) basis representation
• toM(RingElement) -- Monomial (m-) basis representation
• toM(RingElement,SchurRing) -- Monomial (m-) basis representation
• toO -- Expansion in the basis of orthogonal characters
• toO(RingElement) -- Expansion in the basis of orthogonal characters
• toO(RingElement,SchurRing) -- Expansion in the basis of orthogonal characters
• toP -- Power-sum (p-) basis representation
• toP(RingElement) -- Power-sum (p-) basis representation
• toRatGL -- Lift a Schur (GL, SL) character into a rational-GL Schur ring
• toRatGL(RingElement,SchurRing) -- Lift a Schur (GL, SL) character into a rational-GL Schur ring
• toS -- Schur (s-) basis representation
• toS(RingElement) -- Schur (s-) basis representation
• toS(RingElement,SchurRing) -- Schur (s-) basis representation
• toSn -- Promote a Schur-basis element into an Sn character ring
• toSn(RingElement,SchurRing) -- Promote a Schur-basis element into an Sn character ring
• toSp -- Expansion in the basis of symplectic characters
• toSp(RingElement) -- Expansion in the basis of symplectic characters
• toSp(RingElement,SchurRing) -- Expansion in the basis of symplectic characters
• toSymm -- Convert a Schur ring element to an element of the associated symmetric ring
• toSymm(Number) -- Convert a Schur ring element to an element of the associated symmetric ring
• toSymm(RingElement) -- Convert a Schur ring element to an element of the associated symmetric ring