50.20 Restricted

Restricted( tbl, subtbl, chars )
Restricted( tbl, subtbl, chars, specification )
Restricted( chars, fusionmap )

returns the restrictions, i.e. the indirections, of the characters in the list chars by a subgroup fusion map. This map can either be entered directly as fusionmap, or it must be stored on the character table subtbl and must have destination tbl; in the latter case the value of the specification field of the desired fusion may be specified as specification (see GetFusionMap). If no such fusion is stored, false is returned.

More about Maps and Parametrized Maps); any value that is not uniquely determined in a restricted character is set to an unknown (see Unknown); for parametrized indirection of characters, see CompositionMaps.

Restriction and inflation are the same procedures, so Restricted and Inflated are identical, see Inflated.

    gap> s5:= CharTable( "A5.2" );; a5:= CharTable( "A5" );;
    gap> Restricted( s5, a5, s5.irreducibles );
    [ [ 1, 1, 1, 1, 1 ], [ 1, 1, 1, 1, 1 ], [ 6, -2, 0, 1, 1 ],
      [ 4, 0, 1, -1, -1 ], [ 4, 0, 1, -1, -1 ], [ 5, 1, -1, 0, 0 ],
      [ 5, 1, -1, 0, 0 ] ]
    gap> Restricted( s5.irreducibles, [ 1, 6, 2, 6 ] );
                        # restrictions to the cyclic group of order 4
    [ [ 1, 1, 1, 1 ], [ 1, -1, 1, -1 ], [ 6, 0, -2, 0 ], [ 4, 0, 0, 0 ],
      [ 4, 0, 0, 0 ], [ 5, -1, 1, -1 ], [ 5, 1, 1, 1 ] ]

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