Parabolic -- the class of parabolic subgroups of Weyl groups

Methods that use an object of class Parabolic:

• dynkinDiagram(DynkinDiagram,Parabolic) -- the Dynkin diagram of the Levy subgroup of a parabolic
• isMinimalRepresentative(Parabolic,WeylGroupElement) -- check whether an element of a Weyl group is the minimal representative of a right coset
• isMinimalRepresentative(Parabolic,WeylGroupElement,Parabolic) -- check whether an element of a Weyl group is the minimal representative of a double coset
• isMinimalRepresentative(WeylGroupElement,Parabolic) -- check whether an element of a Weyl group is the minimal representative of a left coset
• isRoot(RootSystem,Parabolic,Root) -- check whether a root is in the sub root system of the parabolic
• longestWeylGroupElement(RootSystem,Parabolic) -- the longest element of a parabolic subgroup of the Weyl group of a root system
• Parabolic % WeylGroupElement -- the right coset defined by an element of Weyl group
• Parabolic % WeylGroupLeftCoset -- the double coset defined by a left coset
• Parabolic == Parabolic -- equality of parabolics
• poincareSeries(RootSystem,Parabolic,RingElement) -- the generating series of a quotient of the Weyl group by length
• positiveRoots(RootSystem,Parabolic) -- the set of all positive roots in a parabolic sugroups
• rootSystem(RootSystem,Parabolic) -- the root system of the Levy subgroup of a parabolic
• WeylGroupElement % Parabolic -- the left coset defined by an element of Weyl group
• WeylGroupRightCoset % Parabolic -- the double coset defined by a right coset

For the programmer

The object Parabolic is a type, with ancestor classes Set < Tally < VirtualTally < HashTable < Thing.

The source of this document is in WeylGroups.m2:3311:0.