parabolic(WeylGroupDoubleCoset) -- the parabolic associated to a double coset

Function: parabolic
Usage:

parabolic(d)
Inputs:
- d, an instance of the type WeylGroupDoubleCoset,
Outputs:
- an instance of the type Parabolic, a standard parabolic subgroup corresponding to the coset d as in Carter, Finite Groups of Lie Type, p. 65, thm 2.7.4.

Description

i1 : R=rootSystemA(4)

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

o1 : RootSystem

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

o2 = set {4, 1, 2}

o2 : Parabolic

i3 : w=reduce(R,{3,2,4,3})

o3 = WeylGroupElement{RootSystem{...8...}, |  3 |}
                                           |  1 |
                                           | -3 |
                                           |  1 |

o3 : WeylGroupElement

i4 : d= P % w % P

o4 = WeylGroupDoubleCoset{set {4, 1, 2}, set {4, 1, 2}, WeylGroupElement{RootSystem{...8...}, |  3 |}}
                                                                                              |  1 |
                                                                                              | -3 |
                                                                                              |  1 |

o4 : WeylGroupDoubleCoset

i5 : parabolic(d)

o5 = set {4, 2}

o5 : Parabolic

Ways to use this method:

parabolic(WeylGroupDoubleCoset) -- the parabolic associated to a double coset

The source of this document is in WeylGroups.m2:3383:0.