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Macaulay2 web site
WeylGroups
::
WeylGroupLeftCoset
WeylGroupLeftCoset -- the class of left cosets of Weyl groups by parabolic subgroup
Description
a coset wW
P
is represented by the list consisting of a parabolic subgroup
P
and the representative of minimal length
w
Methods that use an object of class WeylGroupLeftCoset :
intervalBruhat(WeylGroupLeftCoset,WeylGroupLeftCoset)
-- elements between two given ones for the Bruhat order on a quotient of a Weyl group
minimalRepresentative(WeylGroupLeftCoset)
-- the minimal representative of a coset
Parabolic % WeylGroupLeftCoset
-- the double coset defined by a left coset
WeylGroupElement * WeylGroupLeftCoset
-- apply an element of a Weyl group to a left coset
WeylGroupLeftCoset == WeylGroupLeftCoset
-- equality of left cosets
For the programmer
The object
WeylGroupLeftCoset
is
a
type
, with ancestor classes
BasicList
<
Thing
.