JInductionTable( H, W )
JInductionTable
computes the decomposition into irreducible characters
of W of the J-induced of the irreducible characters of H. The
J-induced of chi is the sum of the irreducible components of the
induced of chi which have same a-function (see
LowestPowerGenericDegrees) as chi. In the table the rows correspond
to the characters of the parent group, the columns to those of the
subgroup. What is returned is actually a record with several fields:
scalar
contains the induction table proper, and there is a Display
method. The other fields contain labeling information taken from the
character tables of H and W when it exists.
gap> W := CoxeterGroup( "D", 4 );; gap> H := ReflectionSubgroup( W, [ 1, 3 ] );; gap> Display( JInductionTable( H, W ) ); J-Induction from A2 into D4tt |
111 21 3 ________________ 11.+tt |
. . . 11.-tt |
. . . 1.111tt |
. . . .1111tt |
. . . 11.2tt |
1 . . 1.21tt |
1 . . .211tt |
. . . 2.+tt |
. . . 2.-tt |
. . . .22tt |
. . . 1.3tt |
. 1 . .31tt |
. . . .4tt |
. . 1
This function requires the package "chevie" (see RequirePackage).
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GAP 3.4.4