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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

Given a GKMVariety $X$ created by either generalizedFlagVariety or generalizedSchubertVariety, computes and returns the Bruhat order corresponding to the Bruhat decomposition. The resulting poset is cached in $X$, and can be accessed by either cellOrder or bruhatOrder.

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

Ways to use bruhatOrder :

bruhatOrder(GKMVariety)

For the programmer

The object bruhatOrder is a method function.