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Macaulay2 web site
WeylGroups
::
WeylGroupElement
WeylGroupElement -- the class of elements of Weyl groups
Description
w
is represented by the list consisting of a root system and
w
applied to the half-sum of positive roots
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
.