bruhatOrder -- computes the Bruhat order on a generalized flag variety

Synopsis

• Usage:

  P = bruhatOrder(X)

• Inputs:
  • X, a GKM variety, a generalized flag variety or Schubert variety
• Outputs:
  • P, an instance of the type Poset, the Bruhat order

Description

i1 : Fl3 = generalizedFlagVariety("A",2,{1,2})

o1 = a GKM variety with an action of a 3-dimensional torus

o1 : GKMVariety

i2 : cellOrder Fl3
stdio:2:1:(3): error:  no cell order defined on this moment graph

i2 : P = bruhatOrder Fl3

o2 = P

o2 : Poset

i3 : #(coveringRelations P) == 8

o3 = true

i4 : cellOrder Fl3

o4 = P

o4 : Poset

See also

• cellOrder -- the poset of a stratification of a GKM variety
• generalizedFlagVariety -- makes a generalized flag variety as a GKM variety
• generalizedSchubertVariety -- create a generalized Schubert variety