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SchurFunctors -- for computing Schur functors

Description

This package provides methods for computing Schur functors.

Authors

Version

This documentation describes version 0.1 of SchurFunctors.

Citation

If you have used this package in your research, please cite it as follows:

@misc{SchurFunctorsSource,
  title = {{SchurFunctors: Schur modules and maps between them. Version~0.1}},
  author = {Michael E. Stillman and Anton Leykin and Mauricio Velasco},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

  • Types
    • Filling (missing documentation)
  • Functions and commands
    • augmentFilling (missing documentation)
    • character -- Determines the character of a composition of Schur functors applied to the representation of GL(V) on V
    • characterRep (missing documentation)
    • decomposeRep (missing documentation)
    • printSchurModuleElement (missing documentation)
    • schur -- creates a map between Schur modules
    • schurModule -- creates Schur module from a partition and free module
    • schurModulesMap -- creates a map between two Schur modules via the specified function.
    • splitCharacter -- Decomposes a symmetric polynomial as a sum of Schur functions
    • straighten -- Given a tableau of shape lambda express it as a linear combination of SST in the given Schur module
  • Methods
    • augmentFilling(Filling,ZZ,ZZ) (missing documentation)
    • character(List,ZZ) -- see character -- Determines the character of a composition of Schur functors applied to the representation of GL(V) on V
    • characterRep(Matrix) (missing documentation)
    • conjugate(Filling) (missing documentation)
    • decomposeRep(Matrix) (missing documentation)
    • exchange(Filling,ZZ,ZZ,List) (missing documentation)
    • Filling ? Filling (missing documentation)
    • Filling _ List (missing documentation)
    • net(Filling) (missing documentation)
    • printSchurModuleElement(Vector,Module) (missing documentation)
    • schur(List,Matrix) -- see schur -- creates a map between Schur modules
    • schurModule(List,Module) -- see schurModule -- creates Schur module from a partition and free module
    • schurModulesMap(Module,Module,Function) -- see schurModulesMap -- creates a map between two Schur modules via the specified function.
    • splitCharacter(RingElement) -- see splitCharacter -- Decomposes a symmetric polynomial as a sum of Schur functions
    • straighten(Filling,Module) -- see straighten -- Given a tableau of shape lambda express it as a linear combination of SST in the given Schur module

For the programmer

The object SchurFunctors is a package, defined in SchurFunctors.m2, with auxiliary files in SchurFunctors/.

The source of this document is in SchurFunctors.m2:394:0.