The matrix representation for a permutation is calculated by studying the action of the permutation on the basis of standard polytabloids.
The permuted polytabloids are then written as a linear combination of standard polytabloids using the straightening algorithm.
i1 : p = new Partition from {2,1}
o1 = Partition{2, 1}
o1 : Partition
|
i2 : l = {0,2,1}
o2 = {0, 2, 1}
o2 : List
|
i3 : matrixRepresentation (l,p)
o3 = | 0 1 |
| 1 0 |
2 2
o3 : Matrix QQ <--- QQ
|
i4 : stan = standardTableaux p
o4 = {| 0 1 |, | 0 2 |}
| 2 | | 1 |
o4 : TableauList
|
i5 : matrixRepresentation (l,stan)
o5 = | 0 1 |
| 1 0 |
2 2
o5 : Matrix QQ <--- QQ
|
i6 : matrixRepresentation stan
o6 = HashTable{{0, 1, 2} => | 1 0 | }
| 0 1 |
{0, 2, 1} => | 0 1 |
| 1 0 |
{1, 0, 2} => | 1 0 |
| -1 -1 |
{1, 2, 0} => | 0 1 |
| -1 -1 |
{2, 0, 1} => | -1 -1 |
| 1 0 |
{2, 1, 0} => | -1 -1 |
| 0 1 |
o6 : HashTable
|
The object matrixRepresentation is a method function.