78.4 ReducedRightCosetRepresentatives

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).

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