WeylGroupElement -- the class of elements of Weyl groups

Methods that use an object of class WeylGroupElement:

• aboveBruhat(WeylGroupElement) -- Weyl group elements just above a given one for the Bruhat order
• coxeterLength(WeylGroupElement) -- the length of a reduced decomposition of an element of a Weyl group
• intervalBruhat(WeylGroupElement,WeylGroupElement) -- elements between two given ones for the Bruhat order on a Weyl group
• inverse(WeylGroupElement) -- the inverse to an element of a Weyl group
• isLtBruhat(WeylGroupElement,WeylGroupElement) -- compare two Weyl group elements in the Bruhat order
• 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
• isReduced(BasicList,WeylGroupElement) -- whether an Weyl group element can be multiplied by some simple reflections with length increasing at each step
• isReflection(WeylGroupElement) -- checks whether an element of a Weyl group is a reflection
• Parabolic % WeylGroupElement -- the right coset defined by an element of Weyl group
• reducedDecomposition(WeylGroupElement) -- the reduced decomposition of an element of a Weyl group
• underBruhat(WeylGroupElement) -- Weyl group elements just under a given one for the Bruhat order
• WeylGroupElement % Parabolic -- the left coset defined by an element of Weyl group
• WeylGroupElement * Root -- apply an element of a Weyl group to a root
• WeylGroupElement * Weight -- apply an element of a Weyl group to a weight
• WeylGroupElement * WeylGroupElement -- the product of two elements of a Weyl group
• WeylGroupElement * WeylGroupLeftCoset -- apply an element of a Weyl group to a left coset
• WeylGroupElement == WeylGroupElement -- equality of elements of Weyl groups
• WeylGroupElement ^ ZZ -- the power of an element of a Weyl group
• WeylGroupRightCoset * WeylGroupElement -- apply an element of a Weyl group to a left coset
• whoseReflection(WeylGroupElement) -- the positive root whose reflection is a given element of a Weyl group

For the programmer

The object WeylGroupElement is a type, with ancestor classes BasicList < Thing.

The source of this document is in WeylGroups.m2:2823:0.