plueckerAlgebra -- Pluecker algebra of a (partial) flag variety

Synopsis

• Usage:

  S = plueckerAlgebra L

• Inputs:
  • L, an instance of the type GrMatchingField or an instance of the type FlMatchingField,
• Optional inputs:
  • MonomialOrder => a string, default value "default", either "default" or "none" (supply "none" only if $L$ is not coherent)
• Outputs:
  • S, an instance of the type Subring, generated by minors of a generic matrix of variables

Description

i1 : L = diagonalMatchingField(2, 4)

o1 = Grassmannian Matching Field for Gr(2, 4)

o1 : GrMatchingField

i2 : S = plueckerAlgebra L

o2 = QQ[p_0..p_5], subring of QQ[x_(1,1)..x_(2,4)]

o2 : Subring

i3 : transpose gens S

o3 = {-2} | x_(1,1)x_(2,2)-x_(1,2)x_(2,1) |
     {-2} | x_(1,1)x_(2,3)-x_(1,3)x_(2,1) |
     {-2} | x_(1,2)x_(2,3)-x_(1,3)x_(2,2) |
     {-2} | x_(1,1)x_(2,4)-x_(1,4)x_(2,1) |
     {-2} | x_(1,2)x_(2,4)-x_(1,4)x_(2,2) |
     {-2} | x_(1,3)x_(2,4)-x_(1,4)x_(2,3) |

                            6                     1
o3 : Matrix (QQ[x   ..x   ])  <-- (QQ[x   ..x   ])
                 1,1   2,4             1,1   2,4

See also

• GrMatchingField -- the class of Grassmannian matching fields
• FlMatchingField -- the class of matching fields for partial flag varieties
• plueckerMap -- The ring map of the Pluecker embedding
• Subring -- The type of all subrings

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