# SpechtModule

Macaulay2 package SpechtModule - a package for constructing Specht Modules. SpechtModule calculates many objects related to the irreducible representations of the symmetric functions. This construction is used to implement an algorithm in invariant theory which calculates efficiently the secondary invariants of any permutation group. The main features of the package include a method for calculating the character table of Sn, algorithms for calculating list of tableaux given a partition (tabloids, standard tableaux and semistandard tableaux among others) an implementation of the straightening algorithm which includes an implementation of the garnir element given a tableau an a row descent. Methods for calculating Higher Specht Polynomials which give a basis of the Specht Modules that arrise in the coinvariant ring of Sn which is the quotient k[x1,..,xn]/(Sym(n)+). And finally methods for calculating the secondary invariants described above