ReducedRightCosetRepresentatives( W, H )
returns a list of reduced elements in the Coxeter group W which are
distinguished representatives for the right cosets of the reflection
subgroup H in W. The distinguished representative in the coset H.w
is the unique element in the coset which sends all roots of H to
positive roots (the element returned by ReducedInCoxeterCoset
). It is
also the element of minimal length in the coset. The representatives are
returned in order of increasing length.
gap> W := CoxeterGroup( "B", 3 );; gap> H := ReflectionSubgroup(W, [ 2, 3 ]);; gap> List( ReducedRightCosetRepresentatives( W, H ), > x-> CoxeterWord( W, x ) ); [ [ ], [ 1 ], [ 1, 2 ], [ 1, 2, 1 ], [ 1, 2, 3 ], [ 1, 2, 1, 3 ], [ 1, 2, 1, 3, 2 ], [ 1, 2, 1, 3, 2, 1 ] ]
This function requires the package "chevie" (see RequirePackage).
GAP 3.4.4