fillingToPMMatrix -- QQ matrix of the Filling-to-PM change of basis on a Schur module

Usage:

fillingToPMMatrix(mu, n)
Inputs:
- mu, a list, a partition
- n, an integer
Outputs:
- a matrix, a $\mathbb{Q}$ matrix; rows = PM tableaux of $\mu$, cols = Fillings of $\mu^t$. Entry $(i, j)$ = coefficient of PM tableau $i$ in fillingToPM(filling_j).

Description

Inverse direction of pmToFillingMatrix; same equivariant iso, transposed convention.

i1 : symbolicForm fillingToPMMatrix({2,1}, 3)

     +-----+-----------+
     |+-+-+|3     +-+-+|
o1 = ||0|0||-  *  |0|0||
     ||1| ||4     |1| ||
     |+-+-+|      +-+-+|
     +-----+-----------+
     |+-+-+|3     +-+-+|
     ||0|1||-  *  |0|1||
     ||1| ||2     |1| ||
     |+-+-+|      +-+-+|
     +-----+-----------+
     |+-+-+|1     +-+-+|
     ||0|2||-  *  |0|1||
     ||1| ||2     |2| ||
     |+-+-+|      +-+-+|
     |     |      +-+-+|
     |     |1  *  |0|2||
     |     |      |1| ||
     |     |      +-+-+|
     +-----+-----------+
     |+-+-+|3     +-+-+|
     ||0|0||-  *  |0|0||
     ||2| ||4     |2| ||
     |+-+-+|      +-+-+|
     +-----+-----------+
     |+-+-+|      +-+-+|
     ||0|1||1  *  |0|1||
     ||2| ||      |2| ||
     |+-+-+|      +-+-+|
     |     |1     +-+-+|
     |     |-  *  |0|2||
     |     |2     |1| ||
     |     |      +-+-+|
     +-----+-----------+
     |+-+-+|3     +-+-+|
     ||0|2||-  *  |0|2||
     ||2| ||2     |2| ||
     |+-+-+|      +-+-+|
     +-----+-----------+
     |+-+-+|3     +-+-+|
     ||1|1||-  *  |1|1||
     ||2| ||4     |2| ||
     |+-+-+|      +-+-+|
     +-----+-----------+
     |+-+-+|3     +-+-+|
     ||1|2||-  *  |1|2||
     ||2| ||2     |2| ||
     |+-+-+|      +-+-+|
     +-----+-----------+

For the programmer

The object fillingToPMMatrix is a function closure.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/PieriMaps/doc.m2:848:0.

fillingToPMMatrix -- QQ matrix of the Filling-to-PM change of basis on a Schur module

Description

See also

For the programmer