SchurFunctors : Table of Contents

• SchurFunctors -- Schur and Weyl functors from partitions and Young tableaux
• augmentFilling -- append an entry to a column of a Filling
• augmentWeylFilling -- append an entry to a row of a WeylFilling
• character -- the character of a composition of Schur functors on GL(V)
• characterRep -- extract the character of a polynomial GL-representation from its matrix
• conjugate(Filling) -- transpose of a Young tableau
• conjugate(WeylFilling) -- transpose of a Weyl-stored Young tableau
• decomposeRep -- decompose a polynomial GL-representation into irreducible subspaces
• dividedPower -- divided-power functor on free modules and matrices
• divMult -- multiplication and comultiplication of divided powers
• Filling -- a Young tableau stored column-wise
• isStandard -- test whether a Filling is semistandard
• isWeylStandard -- test whether a WeylFilling is Weyl-semistandard
• maxWeylFilling -- the lex-largest Weyl-standard tableau of given shape
• normalize -- sort each column of a Filling, with Koszul sign
• printSchurModuleElement -- display a Schur-module element as a linear combination of tableaux
• printWeylModuleElement -- display a Weyl-module element as a linear combination of tableaux
• schur -- the Schur functor applied to a matrix
• schurModule -- Schur module of a partition applied to a free module
• schurModulesMap -- build a map between Schur modules from its action on tableaux
• splitCharacter -- decompose a symmetric polynomial into Schur functions
• standardTableaux -- all semistandard Young tableaux of a given shape
• standardWeylTableaux -- all Weyl-semistandard tableaux of a given shape
• straighten -- straighten a filling into a linear combination of semistandard tableaux
• towardWeylStandard -- a single Garnir-style straightening step for Weyl fillings
• weyl -- construct a WeylFilling or apply the Weyl functor to a map
• weylCharacter -- the character of a composition of Weyl functors on GL(V)
• WeylFilling -- a Young tableau stored row-wise for the Weyl-module basis
• weylModule -- Weyl module of a partition applied to a free module
• weylModulesMap -- build a map between Weyl modules from its action on tableaux
• weylNormalize -- sort each row of a WeylFilling into weakly-increasing order
• weylStraighten -- straighten a Weyl filling into a linear combination of Weyl-semistandard tableaux