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).
GAP 3.4.4