fillingToPM -- convert a SchurFunctors column-form Filling to PieriMaps row-form tableaux

Usage:

fillingToPM F
Inputs:
- F, Filling, a SchurFunctors column-form Filling
Outputs:
- a hash table, the image of F under the antisymmetrize-then-symmetrize equivariant map $\wedge^{\lambda'} V \to \mathrm{Sym}^\lambda V$, expressed as a sum of standard PM-form tableaux with rational coefficients (after PieriMaps straightening).

Description

Inverse (up to a uniform scalar) of pmToFilling. Each column of F is wedge-expanded into $V^{\otimes |\lambda|}$ via the column antisymmetrizer (signed sum over permutations, with normalization $1/\prod \lambda'_j!$), reordered by rows, and projected to symmetric (sort) per row. The result is straightened into the standard PM basis.

i1 : needsPackage "SchurFunctors";

i2 : F = new Filling from {{0,2},{1}};

i3 : fillingToPM F

o3 = HashTable{{{0, 1}, {2}} => 1}
                                1
               {{0, 2}, {1}} => -
                                2

o3 : HashTable

For the programmer

The object fillingToPM is a function closure.

The source of this document is in PieriMaps/doc.m2:728:0.

fillingToPM -- convert a SchurFunctors column-form Filling to PieriMaps row-form tableaux

Description

See also

For the programmer