dynkinDiagram(DynkinDiagram,Parabolic) -- the Dynkin diagram of the Levy subgroup of a parabolic

Synopsis

Function: dynkinDiagram
Usage:

dynkinDiagram(D,P)
Inputs:
- D, an instance of the type DynkinDiagram,
- P, an instance of the type Parabolic,
Outputs:
- an instance of the type DynkinDiagram, the Dynkin diagram of the root system of the Levy subgroup of the Parabolic P

Description

i1 : R=rootSystemD(5)

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

o1 : RootSystem

i2 : D1=dynkinDiagram(R)

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

o2 : DynkinDiagram

i3 : P=parabolic(R,set{1,3,4,5})

o3 = set {1, 3, 4, 5}

o3 : Parabolic

i4 : D2=dynkinDiagram(D1,P)

o4 = DynkinDiagram{{{}, {}, {}, {}, {}}, {{3, 4}, {}, {}, {}, {}}, {{2}, {}, {}, {}, {}}, {{2}, {}, {}, {}, {}}}

o4 : DynkinDiagram

i5 : dynkinType(D2)

o5 = DynkinType{{A, 1}, {A, 3}}

o5 : DynkinType

Ways to use this method: