84.2 CoxeterSubCoset

CoxeterSubCoset( WF, r, [w] )

Returns the reflection subcoset of the Coxeter coset WF generated by the reflections with roots specified by r. r is a list of indices specifying a subset of the roots of W where W is the Coxeter group CoxeterGroup(WF). If specified, w must be an element of W such that w*WF.F0Perm normalizes the subroot system generated by r. If absent, the default value for w is (). It is an error, if w*WF.F0Perm does not normalize the subsystem.

    gap> CoxeterSubCoset( CoxeterCoset( CoxeterGroup( "A", 2 ), (1,2) ), 
    >                                                              [ 1 ] );
    Error, must give w, such that w * WF.F0Perm normalizes subroot system.
     in
    CoxeterSubCoset(CoxeterCoset(CoxeterGroup("A", 2), (1,2)), [ 1 ]) 
     called from main loop
    brk> 
    gap> f4coset := CoxeterCoset( CoxeterGroup( "F", 4 ) );
    CoxeterCoset(CoxeterGroup("F", 4))
    gap> w := RepresentativeOperation( CoxeterGroup( f4coset ), 
    >                      [ 1, 2, 9, 16 ], [ 1, 9, 16, 2], OnTuples );;  
    gap> 3d4again := CoxeterSubCoset( f4coset, [ 1, 2, 9, 16], w );
    CoxeterSubCoset(CoxeterCoset(CoxeterGroup("F", 4)), [ 1, 2, 9, 16 ], 
    ( 2, 9,16)( 3, 4,31)( 5,11,18)( 6,13,10)( 7,27,28)( 8,15,12)(14,22,20)
    (17,19,21)(26,33,40)(29,35,42)(30,37,34)(32,39,36)(38,46,44)
    (41,43,45))
    gap> PrintDynkinDiagram( 3d4again );
    phi acts as ( 2, 9,16) on the component below
    D4   9
          \       
           1 - 2
          /
         16 

This function requires the package "chevie" (see RequirePackage).

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