50.42 ContainedCharacters

ContainedCharacters( tbl, constituents, parachar )

returns the set of all characters contained in the parametrized rational character parachar (see More about Maps and Parametrized Maps), that modulo centralizer orders lie in the linear span of the rational characters constituents of the character table tbl and that have nonnegative integral scalar products with all elements of constituents.

Note: This does not imply that an element of the returned list is necessary a linear combination of constituents.

    gap> s:= CharTable( "HSM12" );; hs:= CharTable( "HS" );;
    gap> rat:= RationalizedMat( s.irreducibles );;
    gap> fus:= InitFusion( s, hs );;
    gap> rest:= CompositionMaps( hs.irreducibles[8], fus );;
    gap> ContainedCharacters( s, rat, rest );
    [ [ 231, 7, -9, -9, 6, 15, 15, -1, -1, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0,
          0, 1, 0, 0, 0, 0 ],
      [ 231, 7, -9, 7, 6, 15, 15, -1, -1, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0,
          0, 1, 0, 0, 0, 0 ] ]

ContainedCharacters calls ContainedDecomposables ContainedDecomposables.

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