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getGrMatchingFields -- The Grassmannian matching fields of a Flag matching field

Synopsis

Description

This function returns a list of the GrMatchingFields that are contained within the given FlMatchingField.

i1 : D = diagonalMatchingField({1,2,3}, 6);
 
i2 : getWeightMatrix D

o2 = | 0  0  0 0 0 0 |
     | 6  5  4 3 2 1 |
     | 12 10 8 6 4 2 |

              3       6
o2 : Matrix ZZ  <-- ZZ
 
i3 : netList getGrMatchingFields D

     +----------------------------------------+
o3 = |Grassmannian Matching Field for Gr(1, 6)|
     +----------------------------------------+
     |Grassmannian Matching Field for Gr(2, 6)|
     +----------------------------------------+
     |Grassmannian Matching Field for Gr(3, 6)|
     +----------------------------------------+
 
i4 : D2 = (getGrMatchingFields D)_1;
 
i5 : getWeightMatrix D2

o5 = | 0 0 0 0 0 0 |
     | 6 5 4 3 2 1 |

              2       6
o5 : Matrix ZZ  <-- ZZ

The above example constructs the diagonal matching field for the partial flag variety Fl(123; 6), which contains the data for three distinct Grassmannian matching fields. Each GrMatchingField is a diagonal matching field, which are induced by a submatrix of the original weight matrix that induces the flag matching field.

Ways to use getGrMatchingFields :

For the programmer

The object getGrMatchingFields is a method function.

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