> < ^ Date: Fri, 02 Jun 1995 11:51:00 +0100 (WET)
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
< ^ Subject: Re: Restricted Characters

Dear Mrs. and Mr. Forum,

Jacob Hirbawi writes

I'm trying to look at the restriction of characters of a group on all of
its subgroups. The function "Restricted" seems like the logical choice, but
for some reason I can't get it to work.

Probably the GAP manual does not tell enough details about this problem.
Here is a solution.

# Define the parent group.
group:= PrimitiveGroup( 8, 3 );

# Compute representatives of conjugacy classes of subgroups,
# and their character tables.
subgroups:= List( ConjugacyClassesSubgroups( group ), Representative );;
tables:= List( subgroups, CharTable );;

# Compute (and store) the class fusions into 'group'.
List( subgroups, s -> FusionConjugacyClasses( s, group ) );;

# Compute the restricted characters.
groupchar:= CharTable( group );
restricted:= List( tables,
t -> Restricted( groupchar, t, groupchar.irreducibles ) );

# Example: Compute the decomposition into irreducibles for one subgroup.
subt:= CharTable( subgroups[11] );;
MatScalarProducts( subt, subt.irreducibles, restricted[11] );

Your last sentence indicates that you are aware of the fact that the update
GAP-3.4.2 has been released.
However, the above also works in GAP-3.4.0.

Kind regards
Thomas Breuer

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