84.6 CharTable for Coxeter cosets

CharTable( WF )

This function returns the character table of the Coxeter coset WF (see also the introduction of this Chapter). We call ``characters'' of the Coxeter coset WF with corresponding Coxeter group W the restriction to W F_0 of a set containing one extension of each F_0-invariant character of W to the semidirect product of W with the cyclic group generated by F_0. (We choose, following Lusztig, in each case one non-canonical extension, called the preferred extension.)

The returned record contains almost all components present in the character table of a Coxeter group. But if F_0 is not trivial then there are no components powermap (since powers of elements in the coset need not be in the coset) and orders (if you really need them, use MatXPerm to determine the order of elements in the coset).

    gap> W := CoxeterCoset( CoxeterGroup( "D", 4 ), (1,2,4) );
    CoxeterCoset(CoxeterGroup("D", 4), (1,2,4))
    gap> Display( CharTable( W ) );
    W( 3D4 )

           2   2    2       2        2   2        3        3
           3   1    1       1        .   .        1        1

             C_3 ~A_2 C_3+A_1 ~A_2+A_1 F_4 ~A_2+A_2 F_4(a_1)

    .4         1    1       1        1   1        1        1
    .1111     -1    1       1       -1   1        1        1
    .22        .    2       2        .  -1       -1       -1
    11.2       .    .       .        .  -1        3        3
    1.3        1    1      -1       -1   .       -2        2
    1.111     -1    1      -1        1   .       -2        2
    1.21       .    2      -2        .   .        2       -2 

This function requires the package "chevie" (see RequirePackage). Previous Up Top Next
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