50.21 Inflated

Inflated( factortbl, tbl, chars )
Inflated( factortbl, tbl, chars, specification )
Inflated( chars, fusionmap )

returns the inflations, i.e. the indirections of chars by a factor fusion map. This map can either be entered directly as fusionmap, or it must be stored on the character table tbl and must have destination factortbl; 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 an inflated 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 Restricted.

    gap> s4:= CharTable( "Symmetric", 4 );;
    gap> s3:= CharTableFactorGroup( s4, [3] );;
    gap> s3.irreducibles;
    [ [ 1, -1, 1 ], [ 2, 0, -1 ], [ 1, 1, 1 ] ]
    gap> s4.fusions;
    [ rec(
          map := [ 1, 2, 1, 3, 2 ],
          type := "factor",
          name := [ 'S', '4', '/', '[', ' ', '3', ' ', ']' ] ) ]
    gap> Inflated( s3, s4, s3.irreducibles );
    [ [ 1, -1, 1, 1, -1 ], [ 2, 0, 2, -1, 0 ], [ 1, 1, 1, 1, 1 ] ]

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