isMinimalRepresentative(Parabolic,WeylGroupElement,Parabolic) -- check whether an element of a Weyl group is the minimal representative of a double coset

Function: isMinimalRepresentative
Usage:

minimalRepresentative(P,w,Q)
Inputs:
- P, an instance of the type Parabolic,
- w, an instance of the type WeylGroupElement,
- Q, an instance of the type Parabolic,
Outputs:
- a Boolean value, true if w is the representative of minimal length of a double coset, and false otherwise

Description

i1 : R=rootSystemE(6)

o1 = RootSystem{...8...}

o1 : RootSystem

i2 : P=parabolic(R,set{1,2,3,4,5})

o2 = set {1, 2, 3, 4, 5}

o2 : Parabolic

i3 : Q=parabolic(R,set{2,3,4,5,6})

o3 = set {2, 3, 4, 5, 6}

o3 : Parabolic

i4 : w=minimalRepresentative ((P % (longestWeylGroupElement R)) % Q)

o4 = WeylGroupElement{RootSystem{...8...}, |  1  |}
                                           |  1  |
                                           |  1  |
                                           |  1  |
                                           |  1  |
                                           | -11 |

o4 : WeylGroupElement

i5 : isMinimalRepresentative(P,w,Q)

o5 = true

Ways to use this method:

isMinimalRepresentative(Parabolic,WeylGroupElement,Parabolic) -- check whether an element of a Weyl group is the minimal representative of a double coset

The source of this document is in WeylGroups.m2:3795:0.