SchurRings : Table of Contents

• SchurRings -- Rings representing irreducible representations of general linear or symmetric groups
• centralizerSize -- Size of the centralizer of a permutation
• ClassFunction -- The class of all Class functions
• classFunction -- Converts symmetric function to class function
• classFunction(BasicList) -- Character of irreducible representation of symmetric group
• coefficientRing(SchurRing) -- Coefficient ring of a Schur ring
• degree(ClassFunction) -- Degree of virtual character
• dim(List,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(...,Memoize=>...) -- Store values of the jacobiTrudi function.
• Memoize -- Option to record values of the jacobiTrudi function
• numgens(SchurRing) -- Number of generators of Schur ring.
• partitions(Set,BasicList) -- Partitions of a set
• plethysm -- Plethystic operations on representations
• plethysm(BasicList,RingElement) -- Plethystic operations on representations
• plethysm(RingElement,ClassFunction) -- Plethystic operations on class functions
• pVariable -- Power-sum symmetric functions in a Symmetric ring
• 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.
• 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
• SchurRing -- The class of all Schur rings
• schurRing -- Make a SchurRing
• schurRing(Ring) -- The Schur ring corresponding to a given Symmetric ring.
• SchurRingElement -- A type describing elements of a SchurRing
• SchurRingIndexedVariableTable
• SVariable -- Specifies symbol representing s-functions
• symmetricFunction -- Converts class function to symmetric function
• symmetricRing -- Make a Symmetric ring
• symmetricRing(Ring) -- The Symmetric ring corresponding to a given (Schur) ring.
• toE -- Elementary symmetric (e-) basis representation
• toH -- Complete symmetric (h-) basis representation
• toP -- Power-sum (p-) basis representation
• toS -- Schur (s-) basis representation